# How do you simplify #5i^32 + 7i^11 + 3i^2 - i^17 # in #a + bi# form?

##### 1 Answer

#### Explanation:

First, you need to know that the imaginary number

Let's write out some powers of

This pattern continues...

I encourage you to try it out. It's much easier with a pencil and paper than here with all the codes.

Essentially, for each power you raise

In this problem, we have:

and

Plug these simplified values in your original expression:

and treat

If you're confused about those middle steps, watch a video:

https://goo.gl/a3K93B

Hope that helps! Imaginary numbers are cool!