Complex numbers can be changed in two main ways: by rotating and scaling them. However, these changes can be pretty tricky. Let’s break it down.

1. What are Polar Coordinates?
   To change complex numbers, we need to convert them from rectangular form, which looks like $a + bi$, to polar form, written as $re^{i\theta}$. Here, $r$ stands for the distance from the origin, and $\theta$ is the angle. This switch can be tough for some students to understand.

2. Rotating Complex Numbers:
   When we want to rotate a complex number by a certain angle, we multiply it by $e^{i\phi}$. This step involves using trigonometric functions, which can feel overwhelming.

3. Scaling Complex Numbers:
   Scaling means making the complex number bigger or smaller. We do this by multiplying it by a number $k$. The new position becomes $z' = kz$. Figuring out where it lands can be confusing.

To make these challenges easier, students can try a few different methods. They can practice by visualizing how these changes look on the complex plane. Using computer programs can also help. Starting with simpler examples is a great way to build up confidence.