Simplify (-5+3i)*(1-2i)

$(- 5 + 3 i) \cdot (1 - 2 i)$

Step 1

Expand $(- 5 + 3 i) (1 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$- 5 (1 - 2 i) + 3 i (1 - 2 i)$

Apply the distributive property.

$- 5 \cdot 1 - 5 (- 2 i) + 3 i (1 - 2 i)$

Apply the distributive property.

$- 5 \cdot 1 - 5 (- 2 i) + 3 i \cdot 1 + 3 i (- 2 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 5$ by $1$ .

$- 5 - 5 (- 2 i) + 3 i \cdot 1 + 3 i (- 2 i)$

Multiply $- 2$ by $- 5$ .

$- 5 + 10 i + 3 i \cdot 1 + 3 i (- 2 i)$

Multiply $3$ by $1$ .

$- 5 + 10 i + 3 i + 3 i (- 2 i)$

Multiply $3 i (- 2 i)$ .

Multiply $- 2$ by $3$ .

$- 5 + 10 i + 3 i - 6 i i$

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

$- 5 + 10 i + 3 i - 6 (i^{1} i)$

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

$- 5 + 10 i + 3 i - 6 (i^{1} i^{1})$

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

$- 5 + 10 i + 3 i - 6 i^{1 + 1}$

Add $1$ and $1$ .

$- 5 + 10 i + 3 i - 6 i^{2}$

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

$- 5 + 10 i + 3 i - 6 \cdot - 1$

Multiply $- 6$ by $- 1$ .

$- 5 + 10 i + 3 i + 6$

Add $- 5$ and $6$ .

$1 + 10 i + 3 i$

Add $10 i$ and $3 i$ .

$1 + 13 i$