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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $2$ .

$6 + 3 (- 5 i) + 4 i \cdot 2 + 4 i (- 5 i)$

Multiply $- 5$ by $3$ .

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

Multiply $2$ by $4$ .

$6 - 15 i + 8 i + 4 i (- 5 i)$

Multiply $4 i (- 5 i)$ .

Multiply $- 5$ by $4$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $- 20$ by $- 1$ .

$6 - 15 i + 8 i + 20$

Add $6$ and $20$ .

$26 - 15 i + 8 i$

Add $- 15 i$ and $8 i$ .

$26 - 7 i$