Simplify -9i(-9i+4)+3(8+8i)

$- 9 i (- 9 i + 4) + 3 (8 + 8 i)$

Step 1

Simplify each term.

Apply the distributive property.

$- 9 i (- 9 i) - 9 i \cdot 4 + 3 (8 + 8 i)$

Multiply $- 9 i (- 9 i)$ .

Multiply $- 9$ by $- 9$ .

$81 i i - 9 i \cdot 4 + 3 (8 + 8 i)$

Raise $i$ to the power of $1$ .

$81 (i^{1} i) - 9 i \cdot 4 + 3 (8 + 8 i)$

Raise $i$ to the power of $1$ .

$81 (i^{1} i^{1}) - 9 i \cdot 4 + 3 (8 + 8 i)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$81 i^{1 + 1} - 9 i \cdot 4 + 3 (8 + 8 i)$

Add $1$ and $1$ .

$81 i^{2} - 9 i \cdot 4 + 3 (8 + 8 i)$

$81 i^{2} - 9 i \cdot 4 + 3 (8 + 8 i)$

Multiply $4$ by $- 9$ .

$81 i^{2} - 36 i + 3 (8 + 8 i)$

Simplify each term.

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

$81 \cdot - 1 - 36 i + 3 (8 + 8 i)$

Multiply $81$ by $- 1$ .

$- 81 - 36 i + 3 (8 + 8 i)$

$- 81 - 36 i + 3 (8 + 8 i)$

Apply the distributive property.

$- 81 - 36 i + 3 \cdot 8 + 3 (8 i)$

Multiply $3$ by $8$ .

$- 81 - 36 i + 24 + 3 (8 i)$

Multiply $8$ by $3$ .

$- 81 - 36 i + 24 + 24 i$

$- 81 - 36 i + 24 + 24 i$

Step 2

Simplify by adding terms.

Add $- 81$ and $24$ .

$- 57 - 36 i + 24 i$

Add $- 36 i$ and $24 i$ .

$- 57 - 12 i$

$- 57 - 12 i$

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