Simplify (9-10i)(-8+3i)

$(9 - 10 i) (- 8 + 3 i)$

Step 1

Expand $(9 - 10 i) (- 8 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$9 (- 8 + 3 i) - 10 i (- 8 + 3 i)$

Apply the distributive property.

$9 \cdot - 8 + 9 (3 i) - 10 i (- 8 + 3 i)$

Apply the distributive property.

$9 \cdot - 8 + 9 (3 i) - 10 i \cdot - 8 - 10 i (3 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $- 8$ .

$- 72 + 9 (3 i) - 10 i \cdot - 8 - 10 i (3 i)$

Multiply $3$ by $9$ .

$- 72 + 27 i - 10 i \cdot - 8 - 10 i (3 i)$

Multiply $- 8$ by $- 10$ .

$- 72 + 27 i + 80 i - 10 i (3 i)$

Multiply $- 10 i (3 i)$ .

Multiply $3$ by $- 10$ .

$- 72 + 27 i + 80 i - 30 i i$

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

$- 72 + 27 i + 80 i - 30 (i^{1} i)$

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

$- 72 + 27 i + 80 i - 30 (i^{1} i^{1})$

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

$- 72 + 27 i + 80 i - 30 i^{1 + 1}$

Add $1$ and $1$ .

$- 72 + 27 i + 80 i - 30 i^{2}$

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

$- 72 + 27 i + 80 i - 30 \cdot - 1$

Multiply $- 30$ by $- 1$ .

$- 72 + 27 i + 80 i + 30$

Add $- 72$ and $30$ .

$- 42 + 27 i + 80 i$

Add $27 i$ and $80 i$ .

$- 42 + 107 i$