The IMSUM function is used add or sum two or more complex numbers.

## Contents:

## Syntax

`= IMSUM(`*inumber1, [inumber2], [inumber3],...*)

*inumber1,2,3... -* These are the complex number that you want to add together. The function requires at least one complex number but you can add as many as you need.

They can be supplied as a string (like "3+4i") or as a reference to a cell containing the complex number, but each number must have a real and imaginary part.

*Note: i or j can be used, but the letter must remain consistent throughout each complex number or a #VALUE! error will be returned*

### Explanation

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

This function works by taking each complex number input, breaking it down into its real and imaginary components, summing up all the real components together, and summing up all the imaginary components together.

Then, it combines these summed parts back into a single complex number as the output.

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 real coefficient would be 9, and the imaginary coefficient would be 3.

When adding two complex numbers together, the real components are added separately from the imaginary components. So, '2+3i' + '2+3i' would be 4+6i. The real 2's get added together, and so do the imaginary 3's.

If there are negative numbers, those get added too, but subtract from the total, rather than add.

### Examples

## How to Add Two Complex Numbers Together

Let's say we have table with two columns of complex numbers, and need to add each column together in a third column.

We can use the formula:

`=IMSUM(`*complex_number1, complex_number2)*

Like so to add up each complex number.

## How to Add Multiple Complex Numbers Together

What if we had more than two complex numbers to add? The IMSUM function can handle as many complex numbers as we can throw at it.

If we have a column with 10 complex numbers, we can feed them all into the IMSUM function to sum them all together. Sadly, the IMSUM function can't handle full ranges like A2:A10, so we need to reference each cell directly.

But, once input, the IMSUM function will add all of the real coefficients together, and all of the imaginary coefficients together.