The IMAGINARY function is used to extract the imaginary coefficient of a complex number.

## Contents:

## Syntax

`= IMAGINARY(`*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 IMAGINARY function is part of the "Engineering" group of functions within Excel.

This function is used to extract the imaginary part of a complex number.

A complex number is usually in the form 'a + bi' or sometimes 'a + bj', where **a** is the real part or coefficient, **b** is the imaginary part, and **i** or **j** is the imaginary number or unit.

So, in the complex number '9+3i', the imaginary coefficient would be 3.

### Examples

## How to Extract the Imaginary Coefficient of a Complex Number

Let's say we have table with complex numbers, and need to pull out the imaginary components of each number.

Without the IMAGINARY function, we would have to use a complicated formula to extract the imaginary part of each cell. But, with the IMAGINARY function, we can simply type:

`= IMAGINARY(A2)`

To extract the imaginary coefficient from a complex number held in cell A2.

So if we put that formula alongside our table and reference the complex numbers, we get something that looks like this:

Here, with the IMAGINARY formula in the second column, we can see that the imaginary parts of each complex number are returned correctly, including the + and - signs and decimals.