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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $4$ .

$8 + 2 i - 3 i \cdot 4 - 3 i i$

Multiply $4$ by $- 3$ .

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

Multiply $- 3 i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

Multiply $- 3$ by $- 1$ .

$8 + 2 i - 12 i + 3$

$8 + 2 i - 12 i + 3$

Add $8$ and $3$ .

$11 + 2 i - 12 i$

Subtract $12 i$ from $2 i$ .

$11 - 10 i$

$11 - 10 i$

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