Simplify i^45

$i^{45}$

Step 1

Rewrite $i^{45}$ as ${(i^{4})}^{11} i$ .

Factor out $i^{44}$ .

$i^{44} i$

Rewrite $i^{44}$ as ${(i^{4})}^{11}$ .

${(i^{4})}^{11} i$

${(i^{4})}^{11} i$

Step 2

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

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

${({(i^{2})}^{2})}^{11} i$

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

${({(- 1)}^{2})}^{11} i$

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

$1^{11} i$

$1^{11} i$

Step 3

One to any power is one.

$1 i$

Step 4

Multiply $i$ by $1$ .

$i$

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