# Imagine This!

## Imagine this!

It's amazing what you can do when you go beyond the Real world...

### Vanishing Roots

##### Stage: 4 and 5

If $y=x^2-6x+c$, and we vary $c$, what happens to the roots when $c>9$?

### Opening the Door

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

What happens when we add together two complex numbers?

### Strolling Along

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

What happens when we multiply a complex number by a real or an imaginary number?