Simplify (7-5i)(-2-3i)

$(7 - 5 i) (- 2 - 3 i)$

Step 1

Expand $(7 - 5 i) (- 2 - 3 i)$ using the FOIL Method.

Apply the distributive property.

$7 (- 2 - 3 i) - 5 i (- 2 - 3 i)$

Apply the distributive property.

$7 \cdot - 2 + 7 (- 3 i) - 5 i (- 2 - 3 i)$

Apply the distributive property.

$7 \cdot - 2 + 7 (- 3 i) - 5 i \cdot - 2 - 5 i (- 3 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $- 2$ .

$- 14 + 7 (- 3 i) - 5 i \cdot - 2 - 5 i (- 3 i)$

Multiply $- 3$ by $7$ .

$- 14 - 21 i - 5 i \cdot - 2 - 5 i (- 3 i)$

Multiply $- 2$ by $- 5$ .

$- 14 - 21 i + 10 i - 5 i (- 3 i)$

Multiply $- 5 i (- 3 i)$ .

Multiply $- 3$ by $- 5$ .

$- 14 - 21 i + 10 i + 15 i i$

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

$- 14 - 21 i + 10 i + 15 (i^{1} i)$

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

$- 14 - 21 i + 10 i + 15 (i^{1} i^{1})$

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

$- 14 - 21 i + 10 i + 15 i^{1 + 1}$

Add $1$ and $1$ .

$- 14 - 21 i + 10 i + 15 i^{2}$

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

$- 14 - 21 i + 10 i + 15 \cdot - 1$

Multiply $15$ by $- 1$ .

$- 14 - 21 i + 10 i - 15$

Subtract $15$ from $- 14$ .

$- 29 - 21 i + 10 i$

Add $- 21 i$ and $10 i$ .

$- 29 - 11 i$