Simplify (4-3i)(5+2i)

$(4 - 3 i) (5 + 2 i)$

Step 1

Expand $(4 - 3 i) (5 + 2 i)$ using the FOIL Method.

Apply the distributive property.

$4 (5 + 2 i) - 3 i (5 + 2 i)$

Apply the distributive property.

$4 \cdot 5 + 4 (2 i) - 3 i (5 + 2 i)$

Apply the distributive property.

$4 \cdot 5 + 4 (2 i) - 3 i \cdot 5 - 3 i (2 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $5$ .

$20 + 4 (2 i) - 3 i \cdot 5 - 3 i (2 i)$

Multiply $2$ by $4$ .

$20 + 8 i - 3 i \cdot 5 - 3 i (2 i)$

Multiply $5$ by $- 3$ .

$20 + 8 i - 15 i - 3 i (2 i)$

Multiply $- 3 i (2 i)$ .

Multiply $2$ by $- 3$ .

$20 + 8 i - 15 i - 6 i i$

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

$20 + 8 i - 15 i - 6 (i^{1} i)$

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

$20 + 8 i - 15 i - 6 (i^{1} i^{1})$

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

$20 + 8 i - 15 i - 6 i^{1 + 1}$

Add $1$ and $1$ .

$20 + 8 i - 15 i - 6 i^{2}$

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

$20 + 8 i - 15 i - 6 \cdot - 1$

Multiply $- 6$ by $- 1$ .

$20 + 8 i - 15 i + 6$

Add $20$ and $6$ .

$26 + 8 i - 15 i$

Subtract $15 i$ from $8 i$ .

$26 - 7 i$