Simplify -10i^104+9i^7+4i^100-9i^114

$- 10 i^{104} + 9 i^{7} + 4 i^{100} - 9 i^{114}$

Simplify each term.

Rewrite $i^{104}$ as ${(i^{4})}^{26}$ .

$- 10 {(i^{4})}^{26} + 9 i^{7} + 4 i^{100} - 9 i^{114}$

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

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

$- 10 {({(i^{2})}^{2})}^{26} + 9 i^{7} + 4 i^{100} - 9 i^{114}$

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

$- 10 {({(- 1)}^{2})}^{26} + 9 i^{7} + 4 i^{100} - 9 i^{114}$

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

$- 10 \cdot 1^{26} + 9 i^{7} + 4 i^{100} - 9 i^{114}$

One to any power is one.

$- 10 \cdot 1 + 9 i^{7} + 4 i^{100} - 9 i^{114}$

Multiply $- 10$ by $1$ .

$- 10 + 9 i^{7} + 4 i^{100} - 9 i^{114}$

Rewrite $i^{7}$ as $i^{4} (i^{2} \cdot i)$ .

Factor out $i^{4}$ .

$- 10 + 9 (i^{4} i^{3}) + 4 i^{100} - 9 i^{114}$

Factor out $i^{2}$ .

$- 10 + 9 (i^{4} (i^{2} \cdot i)) + 4 i^{100} - 9 i^{114}$

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

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

$- 10 + 9 ({(i^{2})}^{2} (i^{2} \cdot i)) + 4 i^{100} - 9 i^{114}$

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

$- 10 + 9 ({(- 1)}^{2} (i^{2} \cdot i)) + 4 i^{100} - 9 i^{114}$

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

$- 10 + 9 (1 (i^{2} \cdot i)) + 4 i^{100} - 9 i^{114}$

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

$- 10 + 9 (i^{2} \cdot i) + 4 i^{100} - 9 i^{114}$

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

$- 10 + 9 (- 1 \cdot i) + 4 i^{100} - 9 i^{114}$

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

$- 10 + 9 (- i) + 4 i^{100} - 9 i^{114}$

Multiply $- 1$ by $9$ .

$- 10 - 9 i + 4 i^{100} - 9 i^{114}$

Rewrite $i^{100}$ as ${(i^{4})}^{25}$ .

$- 10 - 9 i + 4 {(i^{4})}^{25} - 9 i^{114}$

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

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

$- 10 - 9 i + 4 {({(i^{2})}^{2})}^{25} - 9 i^{114}$

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

$- 10 - 9 i + 4 {({(- 1)}^{2})}^{25} - 9 i^{114}$

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

$- 10 - 9 i + 4 \cdot 1^{25} - 9 i^{114}$

One to any power is one.

$- 10 - 9 i + 4 \cdot 1 - 9 i^{114}$

Multiply $4$ by $1$ .

$- 10 - 9 i + 4 - 9 i^{114}$

Rewrite $i^{114}$ as ${(i^{4})}^{28} i^{2}$ .

Factor out $i^{112}$ .

$- 10 - 9 i + 4 - 9 (i^{112} i^{2})$

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

$- 10 - 9 i + 4 - 9 ({(i^{4})}^{28} i^{2})$

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

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

$- 10 - 9 i + 4 - 9 ({({(i^{2})}^{2})}^{28} i^{2})$

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

$- 10 - 9 i + 4 - 9 ({({(- 1)}^{2})}^{28} i^{2})$

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

$- 10 - 9 i + 4 - 9 (1^{28} i^{2})$

One to any power is one.

$- 10 - 9 i + 4 - 9 (1 i^{2})$

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

$- 10 - 9 i + 4 - 9 i^{2}$

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

$- 10 - 9 i + 4 - 9 \cdot - 1$

Multiply $- 9$ by $- 1$ .

$- 10 - 9 i + 4 + 9$

Simplify by adding numbers.

Add $- 10$ and $4$ .

$- 6 - 9 i + 9$

Add $- 6$ and $9$ .

$3 - 9 i$

Simplify -10i^104+9i^7+4i^100-9i^114

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