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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $2$ .

$8 + 4 (- 5 i) + 3 i \cdot 2 + 3 i (- 5 i)$

Multiply $- 5$ by $4$ .

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

Multiply $2$ by $3$ .

$8 - 20 i + 6 i + 3 i (- 5 i)$

Multiply $3 i (- 5 i)$ .

Multiply $- 5$ by $3$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $- 15$ by $- 1$ .

$8 - 20 i + 6 i + 15$

Add $8$ and $15$ .

$23 - 20 i + 6 i$

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

$23 - 14 i$