Simplify 2(-36-3i)+(5+2i)(12-2i)

$2 (- 36 - 3 i) + (5 + 2 i) (12 - 2 i)$

Simplify each term.

Apply the distributive property.

$2 \cdot - 36 + 2 (- 3 i) + (5 + 2 i) (12 - 2 i)$

Multiply $2$ by $- 36$ .

$- 72 + 2 (- 3 i) + (5 + 2 i) (12 - 2 i)$

Multiply $- 3$ by $2$ .

$- 72 - 6 i + (5 + 2 i) (12 - 2 i)$

Expand $(5 + 2 i) (12 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$- 72 - 6 i + 5 (12 - 2 i) + 2 i (12 - 2 i)$

Apply the distributive property.

$- 72 - 6 i + 5 \cdot 12 + 5 (- 2 i) + 2 i (12 - 2 i)$

Apply the distributive property.

$- 72 - 6 i + 5 \cdot 12 + 5 (- 2 i) + 2 i \cdot 12 + 2 i (- 2 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $12$ .

$- 72 - 6 i + 60 + 5 (- 2 i) + 2 i \cdot 12 + 2 i (- 2 i)$

Multiply $- 2$ by $5$ .

$- 72 - 6 i + 60 - 10 i + 2 i \cdot 12 + 2 i (- 2 i)$

Multiply $12$ by $2$ .

$- 72 - 6 i + 60 - 10 i + 24 i + 2 i (- 2 i)$

Multiply $2 i (- 2 i)$ .

Multiply $- 2$ by $2$ .

$- 72 - 6 i + 60 - 10 i + 24 i - 4 i i$

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

$- 72 - 6 i + 60 - 10 i + 24 i - 4 (i^{1} i)$

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

$- 72 - 6 i + 60 - 10 i + 24 i - 4 (i^{1} i^{1})$

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

$- 72 - 6 i + 60 - 10 i + 24 i - 4 i^{1 + 1}$

Add $1$ and $1$ .

$- 72 - 6 i + 60 - 10 i + 24 i - 4 i^{2}$

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

$- 72 - 6 i + 60 - 10 i + 24 i - 4 \cdot - 1$

Multiply $- 4$ by $- 1$ .

$- 72 - 6 i + 60 - 10 i + 24 i + 4$

Add $60$ and $4$ .

$- 72 - 6 i + 64 - 10 i + 24 i$

Add $- 10 i$ and $24 i$ .

$- 72 - 6 i + 64 + 14 i$

Simplify by adding terms.

Add $- 72$ and $64$ .

$- 8 - 6 i + 14 i$

Add $- 6 i$ and $14 i$ .

$- 8 + 8 i$

Simplify 2(-36-3i)+(5+2i)(12-2i)

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