Understanding complex numbers can be tough, especially for Year 13 students. Sometimes, visuals can make things more confusing instead of clearer. Let's break it down:

Addition and Subtraction:
When you add complex numbers on an Argand diagram, it should be like adding arrows. However, if students mix up angles and sizes, they can make big mistakes. It can be hard for them to see that adding $z_1 + z_2$ is similar to putting two vectors (or arrows) together.

Multiplication:
Multiplying complex numbers involves both turning (rotation) and growing (scaling). This can feel overwhelming for students. They have to understand how the angle changes and how the size grows, which can be tricky.

Even though these challenges can be tough, there are ways to make it easier:

Practice:
The more you work with examples, the better you understand the material.

Dynamic Software Tools:
Using fun, interactive tools can really help. They show how complex numbers work in a visual way, making it easier to understand and remember, without feeling overwhelmed.

With practice and the right tools, students can feel more confident with complex numbers!