Simplify (-i)^5

${(- i)}^{5}$

Step 1

Apply the product rule to $- i$ .

${(- 1)}^{5} i^{5}$

Step 2

Raise $- 1$ to the power of $5$ .

$- i^{5}$

Step 3

Factor out $i^{4}$ .

$- (i^{4} i)$

Step 4

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

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

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

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

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

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

$- (1 i)$

$- (1 i)$

Step 5

Multiply $i$ by $1$ .

$- i$

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