Simplify 2i^15

$2 i^{15}$

Step 1

Rewrite $i^{15}$ as ${(i^{4})}^{3} (i^{2} \cdot i)$ .

Factor out $i^{12}$ .

$2 (i^{12} i^{3})$

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

$2 ({(i^{4})}^{3} i^{3})$

Factor out $i^{2}$ .

$2 ({(i^{4})}^{3} (i^{2} \cdot i))$

$2 ({(i^{4})}^{3} (i^{2} \cdot i))$

Step 2

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

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

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

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

$2 ({({(- 1)}^{2})}^{3} (i^{2} \cdot i))$

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

$2 (1^{3} (i^{2} \cdot i))$

$2 (1^{3} (i^{2} \cdot i))$

Step 3

One to any power is one.

$2 (1 (i^{2} \cdot i))$

Step 4

Multiply $i^{2} \cdot i$ by $1$ .

$2 (i^{2} \cdot i)$

Step 5

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

$2 (- 1 \cdot i)$

Step 6

Rewrite $- 1 i$ as $- i$ .

$2 (- i)$

Step 7

Multiply $- 1$ by $2$ .

$- 2 i$

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