Simplify i^60-i^112+10i^93-6i^36

$i^{60} - i^{112} + 10 i^{93} - 6 i^{36}$

Simplify each term.

Rewrite $i^{60}$ as ${(i^{4})}^{15}$ .

${(i^{4})}^{15} - i^{112} + 10 i^{93} - 6 i^{36}$

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

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

${({(i^{2})}^{2})}^{15} - i^{112} + 10 i^{93} - 6 i^{36}$

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

${({(- 1)}^{2})}^{15} - i^{112} + 10 i^{93} - 6 i^{36}$

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

$1^{15} - i^{112} + 10 i^{93} - 6 i^{36}$

One to any power is one.

$1 - i^{112} + 10 i^{93} - 6 i^{36}$

Rewrite $i^{112}$ as ${(i^{4})}^{28}$ .

$1 - {(i^{4})}^{28} + 10 i^{93} - 6 i^{36}$

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

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

$1 - {({(i^{2})}^{2})}^{28} + 10 i^{93} - 6 i^{36}$

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

$1 - {({(- 1)}^{2})}^{28} + 10 i^{93} - 6 i^{36}$

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

$1 - 1^{28} + 10 i^{93} - 6 i^{36}$

One to any power is one.

$1 - 1 \cdot 1 + 10 i^{93} - 6 i^{36}$

Multiply $- 1$ by $1$ .

$1 - 1 + 10 i^{93} - 6 i^{36}$

Rewrite $i^{93}$ as ${(i^{4})}^{23} i$ .

Factor out $i^{92}$ .

$1 - 1 + 10 (i^{92} i) - 6 i^{36}$

Rewrite $i^{92}$ as ${(i^{4})}^{23}$ .

$1 - 1 + 10 ({(i^{4})}^{23} i) - 6 i^{36}$

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

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

$1 - 1 + 10 ({({(i^{2})}^{2})}^{23} i) - 6 i^{36}$

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

$1 - 1 + 10 ({({(- 1)}^{2})}^{23} i) - 6 i^{36}$

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

$1 - 1 + 10 (1^{23} i) - 6 i^{36}$

One to any power is one.

$1 - 1 + 10 (1 i) - 6 i^{36}$

Multiply $i$ by $1$ .

$1 - 1 + 10 i - 6 i^{36}$

Rewrite $i^{36}$ as ${(i^{4})}^{9}$ .

$1 - 1 + 10 i - 6 {(i^{4})}^{9}$

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

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

$1 - 1 + 10 i - 6 {({(i^{2})}^{2})}^{9}$

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

$1 - 1 + 10 i - 6 {({(- 1)}^{2})}^{9}$

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

$1 - 1 + 10 i - 6 \cdot 1^{9}$

One to any power is one.

$1 - 1 + 10 i - 6 \cdot 1$

Multiply $- 6$ by $1$ .

$1 - 1 + 10 i - 6$

Simplify the expression.

Subtract $1$ from $1$ .

$0 + 10 i - 6$

Add $0$ and $10 i$ .

$10 i - 6$

Reorder $10 i$ and $- 6$ .

$- 6 + 10 i$

Simplify i^60-i^112+10i^93-6i^36

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