## Related questions with answers

Question

Simplify. $i^{11}$

Solution

VerifiedStep 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}$

$=-1\cdot i$

$=-i$

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