### Vector Walk

Starting with two basic vector steps, which destinations can you reach on a vector walk?

### 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.

# Complex Squares

##### Stage: 5 Challenge Level:

What do you get if you square $a+ib$?

Working backwards:

if $(a+ib)^2$ is real, what relationships must $a$ and $b$ satisfy?
if $(a+ib)^2$ is imaginary, what relationships must $a$ and $b$ satisfy?

What does this look like on an Argand diagram?