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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 3$ by $1$ .

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

Multiply $- 2$ by $- 3$ .

$- 3 + 6 i + 7 i \cdot 1 + 7 i (- 2 i)$

Multiply $7$ by $1$ .

$- 3 + 6 i + 7 i + 7 i (- 2 i)$

Multiply $7 i (- 2 i)$ .

Multiply $- 2$ by $7$ .

$- 3 + 6 i + 7 i - 14 i i$

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

$- 3 + 6 i + 7 i - 14 (i^{1} i)$

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

$- 3 + 6 i + 7 i - 14 (i^{1} i^{1})$

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

$- 3 + 6 i + 7 i - 14 i^{1 + 1}$

Add $1$ and $1$ .

$- 3 + 6 i + 7 i - 14 i^{2}$

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

$- 3 + 6 i + 7 i - 14 \cdot - 1$

Multiply $- 14$ by $- 1$ .

$- 3 + 6 i + 7 i + 14$

Add $- 3$ and $14$ .

$11 + 6 i + 7 i$

Add $6 i$ and $7 i$ .

$11 + 13 i$