Simplify (-5+4i)(2+6i)

$(- 5 + 4 i) (2 + 6 i)$

Step 1

Expand $(- 5 + 4 i) (2 + 6 i)$ using the FOIL Method.

Apply the distributive property.

$- 5 (2 + 6 i) + 4 i (2 + 6 i)$

Apply the distributive property.

$- 5 \cdot 2 - 5 (6 i) + 4 i (2 + 6 i)$

Apply the distributive property.

$- 5 \cdot 2 - 5 (6 i) + 4 i \cdot 2 + 4 i (6 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 5$ by $2$ .

$- 10 - 5 (6 i) + 4 i \cdot 2 + 4 i (6 i)$

Multiply $6$ by $- 5$ .

$- 10 - 30 i + 4 i \cdot 2 + 4 i (6 i)$

Multiply $2$ by $4$ .

$- 10 - 30 i + 8 i + 4 i (6 i)$

Multiply $4 i (6 i)$ .

Multiply $6$ by $4$ .

$- 10 - 30 i + 8 i + 24 i i$

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

$- 10 - 30 i + 8 i + 24 (i^{1} i)$

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

$- 10 - 30 i + 8 i + 24 (i^{1} i^{1})$

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

$- 10 - 30 i + 8 i + 24 i^{1 + 1}$

Add $1$ and $1$ .

$- 10 - 30 i + 8 i + 24 i^{2}$

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

$- 10 - 30 i + 8 i + 24 \cdot - 1$

Multiply $24$ by $- 1$ .

$- 10 - 30 i + 8 i - 24$

Subtract $24$ from $- 10$ .

$- 34 - 30 i + 8 i$

Add $- 30 i$ and $8 i$ .

$- 34 - 22 i$