How to use the IMSQRT Function in Excel

In this article, we will learn about how to use the IMSQRT 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 (iota).

i = √-1

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.

= 2 +√-25

= 2 +√-1*25

= 2 +√-1*√25

= 2 +√-1* 5

= 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 Square root of a complex number (X + iY) is given by

Square root of ( X iY ) = √r Cos (/2) + i √r Sin(/2)


  1. X & Y are the coefficients of the real & imaginary part of the complex number (inumber). 
  2. r is equal to the sum of the square of the real & imaginary part. 

r = √X2 + Y2

  1. Cos & Sin are the trigonometric characters where is equals to the inverse tangent of ( Y / X )

= tan-1( Y / X)


The IMSQRT function returns the complex Square root of the complex number (inumber) having both real & imaginary part.


=IMSQRT (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 Square root of the input complex number (inumber)

Use the formula:


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 Square root of the complex number. The coefficient’s sign of i (iota) is changed. 
Now copy the formula to the other remaining cells using Ctrl + D shortcut key.

As you can see the IMSQRT function formula giving results just fine.
The table show here explains more about the results

inumber Real part (X) Imaginary part (Y) IMSQRT
i = 0 + 1i 0 1 0.70 + 0.70 i
1 = 1 + 0i 1 0 1

Note : 

  1. The formula returns the #NUM! error if the complex number doesn’t have lower case i or j (iota).
  2. The formula returns the #VALUE! Error if the complex number doesn’t have correct complex number format.


Hope you understood how to use IMSQRT 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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