How to use the IMARGUMENT Function in Excel

In this article, we will learn about how to use the IMARGUMENT function in Excel.

COMPLEX number (inumber) in excel derived for mathematical number having real and imaginary coefficients. In mathematics we call it the coefficient of i or j.

i = (-1)1/2
Square root of negative number is not possible, so for calculation purpose, -1is named as imaginary and call it iota (i or j). For calculation of some term like shown below.

A = 2 + (-25)1/2

A = 2 + (-1 * 25)1/2

A = 2 + (-1 * 5 * 5)1/2

A = 2 + 5 * (-1)1/2

X + iY = 2 + 5i

This here equation is Complex number (inumber) having 2 different parts called real part &  imaginary part

The coefficient of iota (i) which is 5 is called as imaginary part and the other part 2 is called the real part of the complex number.

Complex number consists of two parts absolute value & argument .

  1. Absolute value of a complex number is the Square root of sum of squares of the coefficient. Let’s take the format of complex number (inumber).
  2. Argument of a complex number is the tangent of the argument.

Absolute value (X + iY) = (X2+Y2)1/2

Tan-1 (z) = Y / X

z= tan-1(Y / X)

Here X & Y are the coefficients of the real & imaginary part of the complex number (inumber)

The IMARGUMENT function returns the argument in radians of the complex number (inumber) having both real & imaginary part.
Syntax:

=IMARGUMENT (inumber)

inumber : complex number having both real & imaginary

Let’s understand this function using it in an example.
005
Here we have values where we need to extract the argument part of the complex number (inumber)

Use the formula:

=IMARGUMENT (A2)

A2 : complex number (inumber) provided as cell reference.
005
As you can see the complex number having real_num = 4 & imaginary part = 3. The formula returned the absolute value which is 5 here.

IMARGUMENT (4 + 3i) = (42+32)1/2= (16+9)1/2 = 5

Now copy the formula to the other remaining cells using Ctrl + D shortcut key.
006
As you can see the IMARGUMENT function formula giving results just fine.
The table show here explains more about the results

inmuber Real part (X) Imaginary part (Y)
i = 0 + 1i 0 1
1 = 1 + 0i 1 0

Note :

  1. The formula returns the #NUM! error if the complex number doesn’t have lower case i or j (iota).
  2. The function returns the angle in radians. So the angle range is (- ,] i.e. -3.141593.. to +3.141593.. (excluding -3.141593..). = 180 (degrees) = 3.14159.. (radians)
  3. If you want the result in degrees, multiply the result by 180/PI ().

007
Hope you understood how to use IMARGUMENT function and referring cell in Excel. Explore more articles on Excel mathematical functions here. Please feel free to state your query or feedback for the above article.

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