Simplify i^65 - MathMaster

$i^{65}$

Rewrite $i^{65}$ as ${(i^{4})}^{16} i$ .

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Factor out $i^{64}$ .

$i^{64} i$

Rewrite $i^{64}$ as ${(i^{4})}^{16}$ .

${(i^{4})}^{16} i$

Rewrite $i^{4}$ as $1$ .

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Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

${({(i^{2})}^{2})}^{16} i$

Rewrite $i^{2}$ as $- 1$ .

${({(- 1)}^{2})}^{16} i$

Raise $- 1$ to the power of $2$ .

$1^{16} i$

One to any power is one.

$1 i$

Multiply $i$ by $1$ .

$i$

Simplify i^65

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