The IMABS function is used to find the absolute value of a complex number. It takes a complicated formula and turns it into a ready-to-use function.

## Contents:

## Syntax

`= IMABS(`*complex_number*)

*complex_number -* This is the complex number for which you want to find the absolute value. It can be supplied as a string (like "3+4i") or as a reference to a cell containing the complex number.

### Explanation

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

This function takes a complex number, then calculates the square of both the real part, and the imaginary part, adds them up, and then finds the square root of this sum.

## What is the Absolute Value of a Complex Number?

Firstly, to understand the IMABS function, you need to know what a complex number is and what we mean by its absolute value.

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit (iÂ² = -1).

The absolute value (or modulus) of a complex number is the distance of that number from the origin (0,0) in the complex plane. Mathematically, for a complex number a + bi, its absolute value is âˆš(aÂ² + bÂ²).

As an example, if you have the complex number: 3+4i, and wanted to take the absolute value of that number, it would look like âˆš(3Â² + 4Â²), or in Excel terms:

`= SQRT(3^2+4^2)`

### Examples

## How to Find the Absolute Value of a Complex Number

Let's say we have table with complex numbers, and need to find their absolute values.

Without the IMABS function, to find the absolute value of a complex number in cell A2, we would need to use this formula:

`= SQRT(IMREAL(A2)^2+IMAGINARY(A2)^2)`

This formula strips out the real and imaginary parts of a complex number and calculates the absolute value.

But, if we use the IMABS function, this can all be done in one easy step, with one formula.

Simple reference a complex number in your formula, and the function will do the rest.

If you want to use a hardcoded number instead of a cell reference, be sure to wrap the complex number in quotation marks like so:

`= IMABS(`*"3+4i")*