Level: A Level Maths

To add two complex numbers, you must add the real and imaginary parts separately.

## Example

Suppose we have two complex numbers:

${\displaystyle z_{1}=4+3i}$

${\displaystyle z_{2}=-2+4i}$

To add them, we add the real and imaginary parts, like this:

${\displaystyle z_{3}=z_{1}+z_{2}=(4-2)+(3+4)i=2+7i}$

## Vector interpretation

Here are the complex numbers ${\displaystyle z_{1}}$, ${\displaystyle z_{2}}$, and their sum ${\displaystyle z_{3}}$, shown as vectors on an Argand diagram.

The position of ${\displaystyle z_{3}}$ can be found by adding the two vectors for ${\displaystyle z_{1}}$ and ${\displaystyle z_{2}}$, as shown below: