The IMSQRT function returns the square root of a complex number.

## Contents:

## Syntax

`= IMSQRT(`*inumber*)

*inumber -* the complex number for which you want to calculate the square root

### Explanation

The IMSQRT function is part of the "Engineering" group of functions within Excel.

This function is designed solely to calculate the square root of a complex.

Complex numbers have both a real part and an imaginary part, typically represented as "a + bi," where 'a' is the real part and 'b' is the imaginary part. The IMSQRT function allows you to find the square root of such complex numbers.

The IMSQRT function uses the following formula to calculate the square root of a complex number 'a + bi':

If we were to create an Excel function to replicate this equation and the IMSQRT function, it would look like this, assuming the complex number is held in B3:

`=COMPLEX(SQRT((SQRT(IMREAL(B3)^2+IMAGINARY(B3)^2)+IMREAL(B3))/2),SIGN(IMAGINARY(B3))*SQRT((SQRT(IMREAL(B3)^2+IMAGINARY(B3)^2)-IMREAL(B3))/2))`

### Examples

## How to Calculate the Square Root of a Complex Number

Let's say you have a table in Excel with complex numbers and you want to find the square roots of these numbers. Here's an example table:

To calculate the square root of these complex numbers, we can simply drop in the IMSQRT function next to them, and reference the complex numbers.

For the first complex number, 3+4i, the IMSQRT function will return a complex result of 2+i. Here, the real part is 2 and the imaginary part is 1, indicating that the square root of 3 + 4i is a complex number with both real and imaginary components.