Deal with math problem Deal with mathematic question Mathematics . This time, the real part can be written as Re(A * B) = x * m y * n, and the imaginary part as Im(A * B) = x * n + y * m. Remember that complex number calculators use a negative sign in the real part because, at some point, we are faced with the product of two numbers i * i, which by definition is -1. Recommended: Please try your approach on {IDE} first, before moving on to the solution. The real DFT transforms an N point time domain signal into two N/2 + 1 point frequency domain signals. It is common practice to use the letter z to stand for a complex number and write z = a + bi where a is the real part and b is the imaginary part. Arguably, the best app I have on my phone, dISAPPOINTING, great tool for checking your work, love this app, when it comes to maths sessions always used this. Output: Real part: 6, Imaginary part: 8. The imaginary part of a complex number is the real number multiplying i, so . imaginary_part online. i, The unit Imaginary Number ((-1)). This is what is going on with our power. Point B. COMPLEX (real_num, i_num, [suffix]) The COMPLEX function syntax has the following arguments: Real_num Required. Algebraic calculation | Let's denote the first number as F=a+biF = a + biF=a+bi and the second one as G=c+diG = c + diG=c+di. With this function, the calculator allows the online calculation of the real part of a complex number. The imaginary part is the multiple of i. Step 2: Click "Solve" to get all the complex roots of the polynomial or algebraic . The voltage and current are both still sinusoidal, but now the current leads the voltage by 90. But there's one last question: how "big" is a complex number? For example, enter 2*x or 5*x^2, instead of 2x or 5x^2. Choose Find All Complex. Example 4 : ax 2 8x + c = 0 two real solutions An imaginary number is the square root of a negative number. Remarks. Do you remember how to add or subtract two 2D vectors? The real part of the refractive index is rather high, ca. Similarly, b is the imaginary part written as Im(z). Complex numbers can also be entered in the polar form r∠ , where r is the signed module (or length) and is the argument (or angle) of the complex number. Imaginary Part of a Complex Number Description Determine the imaginary part of a complex number . Expert teachers will give you an answer in real-time. COMPLEX number (inumber) in excel derived for mathematical number having real and imaginary coefficients. The real part of the complex number is represented by x, and the imaginary part of the complex number is represented by y. We can equally describe the same vector by its projection on the horizontal and vertical axes as shown. Our complex number calculator (also known as an imaginary number calculator) is an . Subtraction: (3+2i)-(5-3i). The real part is 2 and the imaginary part is 3, so the complex coordinate is (2, 3) where 2 is on the real (or horizontal) axis and 3 is on the imaginary (or vertical) axis. For calculating conjugate of the complex number following z=1+7i, The exponential form is convenient if you are not proficient enough in trigonometric laws or you just prefer to work with powers. When typing the imaginary part of a complex number in the appropriate field of the calculator, make sure that the symbol ' i ', representing the imaginary unit, is adjacent to the numeric part without space. The time domain signal is called just that: the time domain signal. Addition: (3+2i)+(5-3i). Scientific complex number calculator for evaluating mathematical expressions of real, imaginary and complex numbers in rectangular and polar forms showing. But opting out of some of these cookies may have an effect on your browsing experience. Instructions :: All Functions re, real part of complex number. Finally, the opposite side of the triangle corresponds to the imaginary axis and is the Reactive Power (Q) given by Q = V I sin , measured in Volt-Amps Reactive (VAR). Math Games, Copyright (c) 2013-2023 https://www.solumaths.com/en, solumaths : mathematics solutions online | But other than that it's amazing, sometimes you just have to go to a calculator or google,but I still love it. Algebraic calculation | About this page: Cubic equations calculator; The calculator finds real and complex roots of cubic equations with real coefficients a, b, c and d: ax + bx + cx + d = 0 (1) using the . For another, the sum of 3 + i and -1 + 2 i is 2 + 3 i. Figure 3 shows that the same thing happens with a purely inductive load. Example: re (23i) = 2. imaginary part of complex number. Get the best Homework answers from top Homework helpers in the field. Check out 37 similar algebra calculators , What is a complex number? One way to think about math equations is to think of them as a puzzle. Knowing that we can write any complex number using its polar coordinates on that plane: Here sin and cos are basic trigonometric functions. Apart from performing the four basic operations of addition, subtraction, multiplication and division of complex numbers, this complex number calculator can be used to calculate powers and principal roots of complex numbers. However, the naive tan 1 definition does obscure the fact that a complex number with negative real part and negative imaginary part lies in the 3rd quadrant: the range of t a n 1 is [ 2, + 2] which is only radians or 180 degrees wide - it covers only half of the phase space. RapidTables. We derive these formulas from the relations in the right triangle on the complex plane. The horizontal axis is the real (R)axis and the vertical axis is the imaginary (I) axis. For example, you could rewrite i as a real part-- 0 is a real number-- 0 plus i. The real part is implemented in the Wolfram Language as Re[z]. Over the years he has written a number of articles for various electronics publications and occasionally provides consulting services as time allows. (In computer programming, the "atan2" function accounts for these multi-quadrant issues and . The real and imaginary parts of the Fourier coefficients c k are written in this unusual way for convenience in defining the classic Fourier series. The Complex Number Calculator solves complex equations and gives real and imaginary, Scientific complex number calculator for evaluating mathematical expressions of real, imaginary and complex numbers in rectangular and polar forms showing, It will perform addition, subtraction, multiplication, division, raising to power, and also will find the polar form, conjugate, modulus, and inverse of the. Head to our polar coordinates calculator if you want to learn more about this coordination system. Click "Submit." Plot will be shown with Real and Imaginary Axes. A complex number is the fancy name for numbers with both real and imaginary parts. Imaginary numbers calculator. This should be geometrically obvious as well: the Real Line is a subset of the Complex Plane. If we are going to be precise (and we are) we can say that at any instant the instantaneous power Pi = Vi Ii. In this case the current lags the voltage by 90, but the average power is also zero. Step 2: Click the blue arrow to submit. A4. At the following model,the arithmetic operations on complex numbers can be easily managed using the Calculators. a x+iy = a x [cos (y log a) + i sin (y log a)] 6. The step-by-step format is easy to follow and helps readers understand the process. It is represented as z = a + bi. Most loads in AC systems will have some resistive and some reactive component, so one number is not enough to describe power in these cases. The angle \varphi is measured from the X-axis counterclockwise, and it can vary from 000 to 22\pi2 or from -\pi to \pi (depending on convention since both are equivalent). Example: im(2-3i) = -3i. This online calculator will provide you the real part, imaginary part and alternate form of the integrals within the results. . Power companies would like all loads to be resistive (PF = 1) since they must size their transmission networks for the Apparent Power, but only Real Power does useful work at the point of consumption. We also use third-party cookies that help us analyze and understand how you use this website. If the angle is between the two, as in the figure, there will be a real and imaginary part to the quantity. How does the Imaginary Numbers Calculator work? The quantity cos is the Power Factor (PF) and varies from one for a perfectly resistive load, to zero for a perfectly reactive load. And actually, the real numbers are a subset of the complex numbers. When performing simple operations on complex numbers, it is helpful to think of them as vectors. This free imaginary number calculator will simplify any complex expression with step-by-step calculations quickly. Also, we can significantly simplify multiple issues from electronics with complex numbers. In other words, it is a complex number which is written as the product of the real number and the imaginary unit i. He worked for several years in R&D for power electronics and telecommunication companies before moving into management roles. The real coefficient of the complex number. Great since I hate asking for help, this is a great automated math solving app, if I don't get it it simply tells me how to do it and shows me the answer, this app is cool especially when it comes to math it really helps me a lot to do my homework thank you so much math app i can spend my whole day answering my modules. Math is the study of numbers, shapes, and patterns. Definitions and Formulas. (x * m + y * n + (y * mx * n) * i) / (m^2+n^2) we get the following result: Re (A / B) = (a * c + b * d) / (m^2 +n^2), Im(A x B)=(y * m x * n) / (m^2 + n^2). Complex Number Calculator The Complex Number Calculator solves complex equations and gives real and imaginary solutions. If omitted, suffix is assumed to be "i". You could re. An imaginary number is the square root of a negative number. Graphing Calculator | Likewise, imaginary numbers are a subset of the complex numbers. Complex numbers | Multiplication: (3+2i)*(5-3i). This app never disappointed me, i bet a lot of coding went into this app and as a fellow coder id love to see all the code. To add and subtract complex numbers, you just combine the real parts and the imaginary parts, like this: (5 + 3 i) + (2 + 8 i) = (5 + 2) + (3 + 8) i = 7 + 11 i. b 2-4ac < 0. a = a, b = 4 and c = c. 4 2-4ac < 0. sin(1+2i) / ln(3+4i) + atan(1+3i) 4(1.8). To solve a math equation, you need to figure out what the equation is asking for and then use the appropriate operations to solve it. Where Re (A + B) = x + m is part of the sum of real numbers, And Im(A + B) = y + n is part of sum of imaginary number. Experts will give you an answer in real-time, Do i need a graphing calculator for statistics, General solution of each differential equation solver, How to determine sum of arithmetic series, How to find area of a cylinder with diameter and height, Relocation cost of living comparison calculator. It is used to solve problems and to understand the world around us. Returns the smallest (closest to negative infinity) value that is not less than the argument and is an integer. Fractions | Complex numbers can be entered in the rectangular (standard) form a + bi, where a and b are the real part and . In a complex number , is called the "real part" of and is called the "imaginary part." If , the complex number is a real number; if , then the complex number is "purely imaginary." We can graph a complex number on the Cartesian . To calculate the real part of the following complex expression z=`(1+i)/(1-i)`, real_part button already appears, the result 1 is returned. First, the imaginary numbers calculator finds a general formula for the complex power of two numbers, given as A * B. AB = (x + yi) (m + ni) = Since it is not clear how to extend this expression, the complex calculator use F as the polar form of a complex number. real_part online. As you would expect, the sinusoidal voltage across the resistor (green trace) results in a sinusoidal current with the same phase (blue trace). Examples: Input: z = 3 + 4i. Complex Number extends the concept of one-dimensional line to a two-dimensional complex plane and uses the horizontal axis for the real part . Let's have a look at calculations with step-by-step hints: We obtain the following results: Re(F/G)=ac+bdc+d\mathrm{Re}(F / G) = \frac{a \cdot c + b \cdot d}{c + d}Re(F/G)=c+dac+bd, Im(FG)=bcadc+d\mathrm{Im}(F\!\cdot\!G) = \frac{b \cdot c - a \cdot d}{c + d}Im(FG)=c+dbcad. From the source of Wikipedia: Notation, Visualization, Cartesian complex plane, Polar complex plane, Modulus and argument, Complex graphs. Then, it is very simple to subtract and adding complex numbers with complex solutions calculator. Similarly, the length of a vector in the two-dimensional Euclidean plane is the distance between its end and the origin of the coordinate system. And you would be correct. Division: (3+2i)/(5-3i). By taking a step-by-step approach, you can more easily see what's going on and how to solve the problem. One of the main fields of complex number usage is the world of wave functions and harmonic motion. You Ask? Summary : The real part calculator allows you to calculate online the real part of a complex number. If the numbers are: A B = x + yi m + ni = (x m) + (y n) * I, then Re (A B) = x m and Im (A B) = y n. The complex number calculator, add (or subtract) each pair of given components separately! To find the square root of a pure imaginary number we first express the number as ix. So, product of a and c should be > 4. This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. When b=0b = 0b=0, the number is purely real, and if a=0a = 0a=0, we have a purely imaginary number. b=sp.symbols('b',real=True) V=sp.symbols('V',imaginary=True) have no effect, because you overwrite the variables b and V in the lines. For example, the square root of 16 is 4 since 4 x 4 = 16. The imaginary part; im(1+I) Modulus of a complex number; absolute(1+I) The argument; arg(1+I) . We are here to help you with all of your homework needs! Lets take a look at the calculation of theorem: A / B = (x + yi)/(m + ni) =, expand the numerator and denominator by combining the complex numbers of the numerator and denominator. This app is good for learning and understanding your mistakes in math. It's helpful to imagine complex numbers as vectors on that complex plane. In other words, a real number can also be thought of as a complex number in which the non-real part is 0. Maths Exercise Generator | A comprehensive complex number calculator which can be used as a scientific calculator to evaluate mathematical expressions containing real, imaginary and, in general, complex numbers in any form including rectangular (standard) and polar forms. Contact | Real part: re(3+2i) Imaginary part: im(3+2i) Absolute value (magnitude): abs(3+2i) Argument angle (radians): arg(3+2i) Conjugate number: conj(3+2i) See also. Scan; Clarify mathematic equations; Deal with math question; Top Experts; Improve . Real functions | Our complex number calculator (also known as an imaginary number calculator) is an excellent tool for solving, Coordinate geometry class 10 important points, Differential equation general solution complex roots, Expansion and simplification of linear expressions, Find words in the text to match these definitions, How many ways to solve differential equations, How to convert radian into degree in calculator, How to solve a system of equations word problem using matrices, Simultaneous equations using matrices calculator, Solve linear quadratic systems calculator, State cost of living comparison calculator. Love the app I'm 10 and don't really know math but this helps me so much! Solving math problems can be fun and challenging! In terms of itself, where is the complex conjugate of . mathematical operations and function evaluations with imaginary numbers, and in general, complex numbers. If a number is purely imaginary or purely real, then set the other part equal to 0. There are many ways to stay healthy and fit, but some methods are more effective than others. The logarithm of a complex numbers (also known as the complex logarithm) can be worked out the following way: One critical remark: since the phases 1\varphi_11 and 1+2k\varphi_1+2k\pi1+2k are equivalent, the complex logarithm has an infinite number of solutions, and we can write the general result as: ln(z1)+i(1+2k)\ln(|z_1|) + i(\varphi_1+2k\pi)ln(z1)+i(1+2k). Following with notation from the previous section, we can write: This time the real part can be written as Re(FG)=acbd\mathrm{Re}(F\!\cdot\!G) = a\!\cdot\!c - b\!\cdot\!dRe(FG)=acbd, and imaginary part as Im(FG)=ad+bc\mathrm{Im}(F\!\cdot\!G) = a\!\cdot\!d + b\!\cdot\!cIm(FG)=ad+bc. Multiplication: (3+2i)*(5-3i). Simple calculator; Percentage calculator; Math Calculators Complex Number Calculator, For further assistance, please Contact Us. HDL Code Generation Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder. ADVERTISMENT Choose Find All Complex 587 Math Tutors . The modulus (or magnitude) is the length (absolute value) in the complex plane, qualifying the complex number z= a+ib z = a + i b (with a a the real part and b b the imaginary part), it is denoted |z| | z | and is equal to |z|= a2+b2 | z | = a 2 + b 2. Hence, either portion could be 0. The Typeset version of the Im command is I Obtain the Imaginary Part of a Complex Number Enter a complex number: Extract the imaginary part: Commands Used. In it, youll find a rich variety of the kinds of articles and information that exemplify a typical issue of the current magazine. The imaginary part is implemented in the Wolfram Language as Im [ z ]. The first step to solving any problem is to scan it and break it down into smaller pieces. Get the free Complex Number Calculator widget for your website, blog, Wordpress, Blogger, or iGoogle. You can probably tell by inspection that the average power in the resistor will be P = (Vpk Ipk). real part of complex number. This calculator will provide you with a plot and possible intermediate steps of integration by parts. This is similar to combining "like terms" when you add polynomials together: (3 x + 2) + (5 x + 7) = 8 x + 9. complex number Add Complex Numbers Calculator to your website to get the ease of using this calculator directly. conjugate of complex number. As a powerful scientific complex number calculator it can also be used to calculate exponential, logarithmic, trigonometric, hyperbolic, ( Gamma ), ( psi) and ( zeta) functions with imaginary or complex number as arguments. Figure out math questions Math is a subject that can be difficult to understand, but with practice and patience, anyone can learn to figure out math problems. The power waveform is identical to that in Figure 1 but shifted down, so it straddles the horizontal axis. Our complex number calculator (also known as an imaginary number calculator) is an excellent tool for solving basic operations with complex numbers. To solve a math equation, you need to find the value of the variable that makes the equation true. In DC circuits the average value of voltage and current is equal to the instantaneous value so the average power is the same as the instantaneous power yielding the familiar relationship P = V I . The zeroth coefficient equals the signal's average value and is real- valued for real-valued signals: c 0 =a 0. Input: z = 6 - 8i. For instance, this imaginary / complex number calculator easily computes mathematical expressions containing complex numbers from the simplest forms such as Soft Latch Switch Circuit. Circuits DIY (blog), January 28, 2020. https://circuits-diy.com/soft-latch-switch-circuit/. Complex numbers have a lot in common with the Cartesian coordinate system because they are pairs of numbers on a Cartesian complex plane. I've been using math app since high school and even now it still answers every kind of college math problem I give it. example. There is also another way to rewrite this number, using the Euler formula: z=zexp(i)z = |z| \cdot \exp(i)z=zexp(i). Therefore, the absolute value is: AB = | z_1| exp * exp (-_1* d), and the independent variable is: arg(AB) = m + n * ln | z_1|. Ditch The Switch: A Soft Latching Circuit Roundup. Hackaday (blog), June 24, 2019. https://hackaday.com/2019/06/24/ditch-the-switch-a-soft-latching-circuit-roundup/. Example: re(2-3i) = 2. im, imaginary part of complex number. z : When b=0, z is real, when a=0, we say that z is pure imaginary. Real part: x = Re z = -1. That particular function takes two arguments, respectively the real and imaginary components of the polar input value. Math is all about solving equations and finding the right answer. The cosecant calculator is here to help you whenever you're looking for the value of the cosecant function for a given angle. In other words, we can write the complex number as: z=z(cos+isin)z = |z| (\cos\varphi + i\cdot\sin\varphi)z=z(cos+isin). Site map Cartesian coordinates: Cartesian form of imaginary number: z = -1. We can also change them anyway you like - that's all your choice. If the angle is between the two, as in the figure, there will be a real and imaginary part to the quantity. If you have a question, our experts will have an answer for you in no time. We need to think of the voltage and current not just in terms of their value or magnitude, as we do in DC circuits, but also in terms of their phase. The sum of a real number and an imaginary number is known as a complex number. Complex Number Calculator. In short, we can use an expression as z = x + iy, where x is the real part and iy is the imaginary part. Multiplication of complex numbers is done using the same . Recall that the square root of a number is the number that when multiplied by itself yields the original number. For calculating real part of the complex number following z=1+7i, This should . The complex numbers calculator can also determine the imaginary part of a complex expression. Write down any arithmetic combination of complex numbers and the calculator will simplify them, with the steps shown. Enter the equation for which you want to find all complex solutions. Homework Support Solutions. Put differently, the Real set is a subset of the Complex set. For instance, the sum of 5 + 3 i and 4 + 2 i is 9 + 5 i. At the end of this text, you can also find information about the properties of complex numbers (most of which are based on the conjugate or the absolute value of complex numbers) and even some practical applications of them. The value of real part: 1 The value of imaginary part after pressing [SHIFT][=] (Re<->Im): 1.732050808 (i . Complex numbers calculator. Example: re(2-3i) = 2. im, imaginary part of complex number. We call this a vector quantity, and traditionally use bold font to distinguish them from magnitude only (or scalar) quantities. Evaluate an expression with complex numbers using an online calculator. Now what if we have a capacitive load such as in Figure 2. Now, let's move to something more challenging - we want to find how multiplying complex numbers work. For further details I can recommend for example: S. O. Kasap and P. Capper, Springer . To find two parts of ( + i) x+iy . Many physics problems benefit from the power of complex numbers. We can also consider the operations above in the polar notation, say F=z1exp(i1)F = |z_1|\exp(i\varphi_1)F=z1exp(i1), G=z2exp(i2)G = |z_2|\exp(i\varphi_2)G=z2exp(i2). Thread-Based Environment Run code in the background using MATLAB backgroundPool or accelerate code with Parallel Computing Toolbox ThreadPool. Perform operations on complex numbers step by step. : (3-4i)*conj(3-4i). Separation of Exponential Functions. Complex Number Calculator im, imaginary part of complex number. Of course, division is only possible when B 0. The calculator will try to simplify any complex expression, with steps shown. As a powerful scientific complex number calculator it can also be used to calculate exponential, logarithmic, trigonometric, hyperbolic, (Gamma), (psi) and (zeta) functions with imaginary or complex number as arguments. Multiplying by complex numbers is not difficult with the complex calculator. The set of all complex numbers is represented by Z C. The set of all imaginary numbers is expressed as Z C R. Complex numbers are also used to calculate the voltage, current, or resistance in an AC circuit (AC means alternating current). Example: im (23i) = 3i. amazing app, i know you might think it is just to cheat with but it actually shows you the answers, and even sometimes graphs with steps to how it got there. If you don't feel comfortable with it, just use our complex number calculator to ensure the outcome is correct. Complex numbers calculation examples. The way we typically see the data presented on a network analyzer is with a Magnitude vs Frequency plot, and a Phase vs Frequency plot. (x + yi)*(m ni)/((m + ni) * (m ni))= Perform multiplication of complex number in standard form, (x * m x * n * i + y * m * i y * n * i * i) / (c^2 (ni)^2)=, again using the fact that i * i = -1. | z_1| Exp * exp(-_1 * d) * exp (i(_1 * m + n * ln |z_1|)). Perform operations on complex numbers step by step. This category only includes cookies that ensures basic functionalities and security features of the website. A Complex Number is expressed in the form of a + bi where a, b are real numbers and i is the imaginary part. Multiplying complex numbers isn't that scary. Embed this widget . Search Share. Analogically, we can find the difference between these numbers: and now Re(FG)=ac\mathrm{Re}(F - G) = a - cRe(FG)=ac, and Im(FG)=bd\mathrm{Im}(F - G) = b - dIm(FG)=bd. We provide top-quality homework help to students of all levels. This pointer is uniquely defined by its length and the angle \(\) to the real axis (x). With this function, the calculator allows the online calculation of the imaginary part of a complex number. This vector is uniquely defined by the real part and the imaginary part of the complex number \(z\). The lines. This point is 2 + 3i. The suffix for the imaginary component of the complex number. The calculator displays a stepwise solution of multiplication and other basic mathematical expressions. If the voltage and current are out of phase by 90 as for a purely reactive load, the power will only have an imaginary component, and the average power will be zero. Arshad, Areeba. Disable your Adblocker and refresh your web page . To add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts. Example: re(2-3i) = 2. im, imaginary part of complex number. However, an online Scientific Notation Calculator allows you to add, subtract, multiply, and divide numbers in scientific notation. is called the imaginary unit and is defined by the equation i = -1.In other words, i is the square root of minus one (-1). Contact | Any real number is a complex number. In a world where we can get answers to our questions faster than ever before, it's important to have a source that can give us the information we need quickly and accurately. Suffix Optional. C/C++ Code Generation Generate C and C++ code using MATLAB Coder. in electronics), and is defined by: The definition of a complex number zzz is the combination of real aaa and imaginary bib\!\cdot\!ibi parts, so that: Here, both aaa and bbb are classically understood as real numbers. To determine a math equation, one would need to first identify the unknown variable and then use algebra to solve for it. where exp()\exp()exp() is an exponent function, the base of which is the number e\mathrm{e}e. Because of the periodicity property, we can see that: exp(i)=exp[i(+2k)]\exp(i\varphi) = \exp[i(\varphi + 2k\pi)]exp(i)=exp[i(+2k)]. When b=0, z is real, when a=0, we say that z is pure imaginary. Complex numbers modulus and argument calculations: https://www.youtube.com/watch?v=rnWFR7_WNUE&list=PLJ-ma5dJyAqoXpMkDzzpTzmQzFMOOJGJ2&index=3Square root of . Output: Real part: 3, Imaginary part: 4. (1+2i)-(3-4i), If the phase difference between the voltage and current is zero, the resulting power only has a real component, which we see as average power. Real and imaginary parts calculator can be found online or in math books. $-6i$: This is an imaginary number that only contains an imaginary part, $-6i$. Determine math equations. Math Calculators | To answer the question of what is a complex number, we have first to ask: "What is an imaginary number?". Complex numbers calculation examples. Firstly, let's find the general formula for the complex power of two numbers, given as FGF^GFG. Use this free circumference calculator to find the area, circumference and diameter of a circle. Every complex number \(z\) can be represented as a vector in the Gaussian number plane. enter real_part(`(1+i)/(1-i)`) or directly A nonzero complex number with zero real part is called an imaginary number or sometimes, for emphasis, a purely imaginary number. Example: re(2-3i) = 2. im, imaginary part of complex number. If the phase angle was 90, the projection on the real axis would be zero, and the imaginary part would be equal to the magnitude. Subtraction: (3+2i)-(5-3i). Description : Writing z = a + ib where a and b are real is called algebraic form of a complex number z : a is the real part of z; ; b is the imaginary part of z. A complex number calculator is a scientific calculator that is also capable of performing In the given expression a is the real part and b is the imaginary part of the complex number.