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

Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

1st Edition•ISBN: 9780076611294Chicha Lynch, Eugene Olmstead

8,789 solutions

1st Edition•ISBN: 9780328931576Al Cuoco, Christine D. Thomas, Danielle Kennedy, Eric Milou, Rose Mary Zbiek

3,653 solutions

4th Edition•ISBN: 9781602773011Saxon

5,377 solutions

1st Edition•ISBN: 9781680330687Boswell, Larson

4,539 solutions