Transformations can help us understand how complex numbers relate to each other by using different shapes and movements. Here are some important types of transformations:

1. Translation: This moves points around in the complex number space. You can think of it as adding a number, written as $z + a$, where $a$ is another complex number.

2. Scaling: This changes the size of the points by multiplying. When you multiply by $a$, if the size of $a$ is bigger than 1 (|a| > 1), the point gets larger. If it's smaller than 1 (|a| < 1), the point shrinks.

3. Rotation: This changes the direction of points by multiplying by $e^{i\theta}$. This helps to shift how a point points, almost like turning it around.

These methods really help us see how complex numbers work together and how they relate to each other in space.