 # How to use the IMCONJUGATE Function in Excel

A 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 (iota).

i = (-1)1/2

The square root of a negative number is not possible, so for calculation purpose, i is 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 a 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 (inumber) is written in the X + iY format.
Complex conjugate of a complex number (X + iY) is given by

X + iY = X - iY (complex conjugate of each other)

X - iY = X + iY (complex conjugate of each other)

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

NOTE : Just change the sign of coefficient of i (iota) to get the complex conjugate of the complex number.

The IMCONJUGATE function returns the complex conjugate of the complex number (inumber) having both real & imaginary part.

Syntax:

=IMCONJUGATE (inumber)

inumber : complex number having both real & imaginary

Let’s understand this function using it in an example. Here we have values where we need to get the complex conjugate of the input complex number (inumber)

Use the formula:

=IMCONJUGATE (A2)

A2 : complex number (inumber) provided as cell reference. As you can see the complex number having real_num = 4 & imaginary part = 3. The formula returns the complex conjugate of the complex number. The coefficient’s sign of i (iota) is changed.

COMPLEX CONJUGATE (4 + 3i) = 4 - 3i

Now copy the formula to the other remaining cells using Ctrl + D shortcut key. As you can see the IMCONJUGATE function formula giving results just fine.

The table show here explains more about the results

 inumber Real part (X) Imaginary part (Y) IMCONJUGATE i = 0 + 1i 0 1 -i 1 = 1 + 0i 1 0 1

Note :
The formula returns the #NUM! error if the complex number doesn’t have lower case i or j (iota).

Hope you understood how to use IMCONJUGATE 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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