# How do you simplify #i^17#?

##### 2 Answers

You should write

#### Explanation:

Any problem of type

**Case 1: when #n# is even**

Rewrite it as

Example to understand this case

**Case 2: when #n# is odd**

Rewrite

Apply the case(1) rules this time using

#i^17 = i#

#### Explanation:

First note that

In general note that if

#i^n = i^(4k+c) = i^(4k)i^c = (i^4)^k i^c = 1^k i^c = i^c#

In our case we can take

#i^17=i^(16+1)=i^16 i^1 = (i^4)^4 i = 1^4 i = i#