Simplify (8-2i^4)+(3-7i^8)-(4+i^9)

$(8 - 2 i^{4}) + (3 - 7 i^{8}) - (4 + i^{9})$

Remove parentheses.

$8 - 2 i^{4} + 3 - 7 i^{8} - (4 + i^{9})$

Simplify each term.

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

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

$8 - 2 {(i^{2})}^{2} + 3 - 7 i^{8} - (4 + i^{9})$

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

$8 - 2 {(- 1)}^{2} + 3 - 7 i^{8} - (4 + i^{9})$

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

$8 - 2 \cdot 1 + 3 - 7 i^{8} - (4 + i^{9})$

$8 - 2 \cdot 1 + 3 - 7 i^{8} - (4 + i^{9})$

Multiply $- 2$ by $1$ .

$8 - 2 + 3 - 7 i^{8} - (4 + i^{9})$

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

$8 - 2 + 3 - 7 {(i^{4})}^{2} - (4 + i^{9})$

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

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

$8 - 2 + 3 - 7 {({(i^{2})}^{2})}^{2} - (4 + i^{9})$

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

$8 - 2 + 3 - 7 {({(- 1)}^{2})}^{2} - (4 + i^{9})$

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

$8 - 2 + 3 - 7 \cdot 1^{2} - (4 + i^{9})$

$8 - 2 + 3 - 7 \cdot 1^{2} - (4 + i^{9})$

One to any power is one.

$8 - 2 + 3 - 7 \cdot 1 - (4 + i^{9})$

Multiply $- 7$ by $1$ .

$8 - 2 + 3 - 7 - (4 + i^{9})$

Simplify each term.

Rewrite $i^{9}$ as ${(i^{4})}^{2} i$ .

Factor out $i^{8}$ .

$8 - 2 + 3 - 7 - (4 + i^{8} i)$

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

$8 - 2 + 3 - 7 - (4 + {(i^{4})}^{2} i)$

$8 - 2 + 3 - 7 - (4 + {(i^{4})}^{2} i)$

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

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

$8 - 2 + 3 - 7 - (4 + {({(i^{2})}^{2})}^{2} i)$

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

$8 - 2 + 3 - 7 - (4 + {({(- 1)}^{2})}^{2} i)$

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

$8 - 2 + 3 - 7 - (4 + 1^{2} i)$

$8 - 2 + 3 - 7 - (4 + 1^{2} i)$

One to any power is one.

$8 - 2 + 3 - 7 - (4 + 1 i)$

Multiply $i$ by $1$ .

$8 - 2 + 3 - 7 - (4 + i)$

$8 - 2 + 3 - 7 - (4 + i)$

Apply the distributive property.

$8 - 2 + 3 - 7 - 1 \cdot 4 - i$

Multiply $- 1$ by $4$ .

$8 - 2 + 3 - 7 - 4 - i$

$8 - 2 + 3 - 7 - 4 - i$

Simplify by adding and subtracting.

Subtract $2$ from $8$ .

$6 + 3 - 7 - 4 - i$

Add $6$ and $3$ .

$9 - 7 - 4 - i$

Subtract $7$ from $9$ .

$2 - 4 - i$

Subtract $4$ from $2$ .

$- 2 - i$

$- 2 - i$

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