Simplify (-3+2i)*(2+i)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$- 3 \cdot 2 - 3 i + 2 i \cdot 2 + 2 i i$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 3$ by $2$ .

$- 6 - 3 i + 2 i \cdot 2 + 2 i i$

Multiply $2$ by $2$ .

$- 6 - 3 i + 4 i + 2 i i$

Multiply $2 i i$ .

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

$- 6 - 3 i + 4 i + 2 (i^{1} i)$

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

$- 6 - 3 i + 4 i + 2 (i^{1} i^{1})$

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

$- 6 - 3 i + 4 i + 2 i^{1 + 1}$

Add $1$ and $1$ .

$- 6 - 3 i + 4 i + 2 i^{2}$

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

$- 6 - 3 i + 4 i + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$- 6 - 3 i + 4 i - 2$

Subtract $2$ from $- 6$ .

$- 8 - 3 i + 4 i$

Add $- 3 i$ and $4 i$ .

$- 8 + i$