Simplify (-i)^12

${(- i)}^{12}$

Step 1

Apply the product rule to $- i$ .

${(- 1)}^{12} i^{12}$

Step 2

Raise $- 1$ to the power of $12$ .

$1 i^{12}$

Step 3

Multiply $i^{12}$ by $1$ .

$i^{12}$

Step 4

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

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

Step 5

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

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

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

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

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

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

$1^{3}$

$1^{3}$

Step 6

One to any power is one.

$1$

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