Try the fastest way to create flashcards
Question

# Simplify. $i^{11}$

Solution

Verified
Step 1
1 of 2

$i^{11}$

We want to rewrite power in the form of $2n+k$, where $n$ and $k$ are integers, such that $k$ is either 0 or 1.

Note that $11=10+1=2\cdot 5+1$, therefore

$i^{11}=i^{2\cdot 5+1}$

$\text{\color{#c34632}Recall that: a^{m+n}=a^m\cdot a^n}$

$i^{2\cdot 5+1}=i^{2\cdot 5}\cdot i^1$

$\text{\color{#c34632}Recall that: a^{m\cdot n}=(a^m)^n}$

$i^{2\cdot 5}\cdot i^1=(i^{2})^{5}\cdot i^1$

$=(-1)^{5}\cdot i$

$\text{\color{#c34632}Recall that: (-1)^{n}=-1 if n is odd}$

$=-1\cdot i$

$=-i$

## Recommended textbook solutions

#### Tennessee Bridge Math

1st EditionISBN: 9780076611294Chicha Lynch, Eugene Olmstead
8,789 solutions

#### enVision Algebra 1

1st EditionISBN: 9780328931576Al Cuoco, Christine D. Thomas, Danielle Kennedy, Eric Milou, Rose Mary Zbiek
3,653 solutions

#### Algebra 1

4th EditionISBN: 9781602773011Saxon
5,377 solutions

#### Big Ideas Math Integrated Mathematics II

1st EditionISBN: 9781680330687Boswell, Larson
4,539 solutions