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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $4$ .

$12 + 3 i - 2 i \cdot 4 - 2 i i$

Multiply $4$ by $- 2$ .

$12 + 3 i - 8 i - 2 i i$

Multiply $- 2 i i$ .

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

$12 + 3 i - 8 i - 2 (i^{1} i)$

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

$12 + 3 i - 8 i - 2 (i^{1} i^{1})$

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

$12 + 3 i - 8 i - 2 i^{1 + 1}$

Add $1$ and $1$ .

$12 + 3 i - 8 i - 2 i^{2}$

$12 + 3 i - 8 i - 2 i^{2}$

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

$12 + 3 i - 8 i - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$12 + 3 i - 8 i + 2$

$12 + 3 i - 8 i + 2$

Add $12$ and $2$ .

$14 + 3 i - 8 i$

Subtract $8 i$ from $3 i$ .

$14 - 5 i$

$14 - 5 i$

Related Questions