Evaluate i^58*i^55

$i^{58} \cdot i^{55}$

Rewrite $i^{58}$ as ${(i^{4})}^{14} i^{2}$ .

Factor out $i^{56}$ .

$i^{56} i^{2} \cdot i^{55}$

Rewrite $i^{56}$ as ${(i^{4})}^{14}$ .

${(i^{4})}^{14} i^{2} \cdot i^{55}$

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

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

${({(i^{2})}^{2})}^{14} i^{2} \cdot i^{55}$

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

${({(- 1)}^{2})}^{14} i^{2} \cdot i^{55}$

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

$1^{14} i^{2} \cdot i^{55}$

One to any power is one.

$1 i^{2} \cdot i^{55}$

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

$i^{2} \cdot i^{55}$

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

$- 1 \cdot i^{55}$

Rewrite $i^{55}$ as ${(i^{4})}^{13} (i^{2} \cdot i)$ .

Factor out $i^{52}$ .

$- 1 \cdot (i^{52} i^{3})$

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

$- 1 \cdot ({(i^{4})}^{13} i^{3})$

Factor out $i^{2}$ .

$- 1 \cdot ({(i^{4})}^{13} (i^{2} \cdot i))$

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

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

$- 1 \cdot ({({(i^{2})}^{2})}^{13} (i^{2} \cdot i))$

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

$- 1 \cdot ({({(- 1)}^{2})}^{13} (i^{2} \cdot i))$

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

$- 1 \cdot (1^{13} (i^{2} \cdot i))$

One to any power is one.

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

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

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

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

$- 1 \cdot (- 1 \cdot i)$

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

$- 1 \cdot (- i)$

Multiply $- 1$ by $- 1$ .

$1 i$

Multiply $i$ by $1$ .

$i$