Simplify i^52

$i^{52}$

Rewrite $i^{52}$ as ${(i^{4})}^{13}$ .

${(i^{4})}^{13}$

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

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

${({(i^{2})}^{2})}^{13}$

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

${({(- 1)}^{2})}^{13}$

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

$1^{13}$

$1^{13}$

One to any power is one.

$1$

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