Simplify i^12+1

$i^{12} + 1$

Step 1

Simplify each term.

Rewrite $i^{12}$ as ${(i^{4})}^{3}$ .

${(i^{4})}^{3} + 1$

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

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

${({(i^{2})}^{2})}^{3} + 1$

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

${({(- 1)}^{2})}^{3} + 1$

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

$1^{3} + 1$

$1^{3} + 1$

One to any power is one.

$1 + 1$

$1 + 1$

Step 2

Add $1$ and $1$ .

$2$

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