Simplify -9i^116-7i^28-7i^95+10i^24

$- 9 i^{116} - 7 i^{28} - 7 i^{95} + 10 i^{24}$

Step 1

Simplify each term.

Rewrite $i^{116}$ as ${(i^{4})}^{29}$ .

$- 9 {(i^{4})}^{29} - 7 i^{28} - 7 i^{95} + 10 i^{24}$

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

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

$- 9 {({(i^{2})}^{2})}^{29} - 7 i^{28} - 7 i^{95} + 10 i^{24}$

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

$- 9 {({(- 1)}^{2})}^{29} - 7 i^{28} - 7 i^{95} + 10 i^{24}$

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

$- 9 \cdot 1^{29} - 7 i^{28} - 7 i^{95} + 10 i^{24}$

One to any power is one.

$- 9 \cdot 1 - 7 i^{28} - 7 i^{95} + 10 i^{24}$

Multiply $- 9$ by $1$ .

$- 9 - 7 i^{28} - 7 i^{95} + 10 i^{24}$

Rewrite $i^{28}$ as ${(i^{4})}^{7}$ .

$- 9 - 7 {(i^{4})}^{7} - 7 i^{95} + 10 i^{24}$

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

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

$- 9 - 7 {({(i^{2})}^{2})}^{7} - 7 i^{95} + 10 i^{24}$

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

$- 9 - 7 {({(- 1)}^{2})}^{7} - 7 i^{95} + 10 i^{24}$

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

$- 9 - 7 \cdot 1^{7} - 7 i^{95} + 10 i^{24}$

One to any power is one.

$- 9 - 7 \cdot 1 - 7 i^{95} + 10 i^{24}$

Multiply $- 7$ by $1$ .

$- 9 - 7 - 7 i^{95} + 10 i^{24}$

Rewrite $i^{95}$ as ${(i^{4})}^{23} (i^{2} \cdot i)$ .

Factor out $i^{92}$ .

$- 9 - 7 - 7 (i^{92} i^{3}) + 10 i^{24}$

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

$- 9 - 7 - 7 ({(i^{4})}^{23} i^{3}) + 10 i^{24}$

Factor out $i^{2}$ .

$- 9 - 7 - 7 ({(i^{4})}^{23} (i^{2} \cdot i)) + 10 i^{24}$

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

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

$- 9 - 7 - 7 ({({(i^{2})}^{2})}^{23} (i^{2} \cdot i)) + 10 i^{24}$

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

$- 9 - 7 - 7 ({({(- 1)}^{2})}^{23} (i^{2} \cdot i)) + 10 i^{24}$

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

$- 9 - 7 - 7 (1^{23} (i^{2} \cdot i)) + 10 i^{24}$

One to any power is one.

$- 9 - 7 - 7 (1 (i^{2} \cdot i)) + 10 i^{24}$

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

$- 9 - 7 - 7 (i^{2} \cdot i) + 10 i^{24}$

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

$- 9 - 7 - 7 (- 1 \cdot i) + 10 i^{24}$

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

$- 9 - 7 - 7 (- i) + 10 i^{24}$

Multiply $- 1$ by $- 7$ .

$- 9 - 7 + 7 i + 10 i^{24}$

Rewrite $i^{24}$ as ${(i^{4})}^{6}$ .

$- 9 - 7 + 7 i + 10 {(i^{4})}^{6}$

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

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

$- 9 - 7 + 7 i + 10 {({(i^{2})}^{2})}^{6}$

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

$- 9 - 7 + 7 i + 10 {({(- 1)}^{2})}^{6}$

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

$- 9 - 7 + 7 i + 10 \cdot 1^{6}$

One to any power is one.

$- 9 - 7 + 7 i + 10 \cdot 1$

Multiply $10$ by $1$ .

$- 9 - 7 + 7 i + 10$

Step 2

Simplify by adding and subtracting.

Subtract $7$ from $- 9$ .

$- 16 + 7 i + 10$

Add $- 16$ and $10$ .

$- 6 + 7 i$

Simplify -9i^116-7i^28-7i^95+10i^24

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