Simplify i^52-i^48

$i^{52} - i^{48}$

Step 1

Simplify each term.

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

${(i^{4})}^{13} - i^{48}$

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

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

${({(i^{2})}^{2})}^{13} - i^{48}$

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

${({(- 1)}^{2})}^{13} - i^{48}$

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

$1^{13} - i^{48}$

$1^{13} - i^{48}$

One to any power is one.

$1 - i^{48}$

Rewrite $i^{48}$ as ${(i^{4})}^{12}$ .

$1 - {(i^{4})}^{12}$

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

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

$1 - {({(i^{2})}^{2})}^{12}$

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

$1 - {({(- 1)}^{2})}^{12}$

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

$1 - 1^{12}$

$1 - 1^{12}$

One to any power is one.

$1 - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$1 - 1$

$1 - 1$

Step 2

Subtract $1$ from $1$ .

$0$

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