### Thousand Words

Here the diagram says it all. Can you find the diagram?

### Complex Squares

What happens when we square complex numbers? Can the square of a complex number be real?

### A Brief Introduction to Complex Numbers

In this problem, we define complex numbers and invite you to explore what happens when you add and multiply them.

# A Brief Introduction to the Argand Diagram

##### Stage: 4 and 5 Challenge Level:

Pick a point for $z_1$ such as $2+i$. Move $z_2$ around, and keep a record of the points where $z_3$ is on the x-axis. What do you notice about the coordinates of $z_2$ and $z_3$?

Repeat for some other points.