Simplify (3-2i)(1+7i)

$(3 - 2 i) (1 + 7 i)$

Step 1

Expand $(3 - 2 i) (1 + 7 i)$ using the FOIL Method.

Apply the distributive property.

$3 (1 + 7 i) - 2 i (1 + 7 i)$

Apply the distributive property.

$3 \cdot 1 + 3 (7 i) - 2 i (1 + 7 i)$

Apply the distributive property.

$3 \cdot 1 + 3 (7 i) - 2 i \cdot 1 - 2 i (7 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $1$ .

$3 + 3 (7 i) - 2 i \cdot 1 - 2 i (7 i)$

Multiply $7$ by $3$ .

$3 + 21 i - 2 i \cdot 1 - 2 i (7 i)$

Multiply $- 2$ by $1$ .

$3 + 21 i - 2 i - 2 i (7 i)$

Multiply $- 2 i (7 i)$ .

Multiply $7$ by $- 2$ .

$3 + 21 i - 2 i - 14 i i$

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

$3 + 21 i - 2 i - 14 (i^{1} i)$

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

$3 + 21 i - 2 i - 14 (i^{1} i^{1})$

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

$3 + 21 i - 2 i - 14 i^{1 + 1}$

Add $1$ and $1$ .

$3 + 21 i - 2 i - 14 i^{2}$

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

$3 + 21 i - 2 i - 14 \cdot - 1$

Multiply $- 14$ by $- 1$ .

$3 + 21 i - 2 i + 14$

Add $3$ and $14$ .

$17 + 21 i - 2 i$

Subtract $2 i$ from $21 i$ .

$17 + 19 i$