How to Use the IMAGINARY Function

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

Contents:

1. Syntax

2. Explanation

3. Example

3.1. Extracting Imaginary Coefficient of a Complex Number

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.