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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $3$ .

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

Multiply $- 4$ by $2$ .

$6 - 8 i + i \cdot 3 + i (- 4 i)$

Move $3$ to the left of $i$ .

$6 - 8 i + 3 \cdot i + i (- 4 i)$

Multiply $i (- 4 i)$ .

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

$6 - 8 i + 3 i - 4 (i^{1} i)$

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

$6 - 8 i + 3 i - 4 (i^{1} i^{1})$

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

$6 - 8 i + 3 i - 4 i^{1 + 1}$

Add $1$ and $1$ .

$6 - 8 i + 3 i - 4 i^{2}$

$6 - 8 i + 3 i - 4 i^{2}$

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

$6 - 8 i + 3 i - 4 \cdot - 1$

Multiply $- 4$ by $- 1$ .

$6 - 8 i + 3 i + 4$

$6 - 8 i + 3 i + 4$

Add $6$ and $4$ .

$10 - 8 i + 3 i$

Add $- 8 i$ and $3 i$ .

$10 - 5 i$

$10 - 5 i$

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