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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $5$ .

$15 + 3 (- 2 i) + 4 i \cdot 5 + 4 i (- 2 i)$

Multiply $- 2$ by $3$ .

$15 - 6 i + 4 i \cdot 5 + 4 i (- 2 i)$

Multiply $5$ by $4$ .

$15 - 6 i + 20 i + 4 i (- 2 i)$

Multiply $4 i (- 2 i)$ .

Multiply $- 2$ by $4$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $- 8$ by $- 1$ .

$15 - 6 i + 20 i + 8$

Add $15$ and $8$ .

$23 - 6 i + 20 i$

Add $- 6 i$ and $20 i$ .

$23 + 14 i$