Write in Standard Form (5-8i)-2i(2-3i)

$(5 - 8 i) - 2 i (2 - 3 i)$

Simplify each term.

Apply the distributive property.

$5 - 8 i - 2 i \cdot 2 - 2 i (- 3 i)$

Multiply $2$ by $- 2$ .

$5 - 8 i - 4 i - 2 i (- 3 i)$

Multiply $- 2 i (- 3 i)$ .

Multiply $- 3$ by $- 2$ .

$5 - 8 i - 4 i + 6 i i$

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

$5 - 8 i - 4 i + 6 (i^{1} i)$

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

$5 - 8 i - 4 i + 6 (i^{1} i^{1})$

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

$5 - 8 i - 4 i + 6 i^{1 + 1}$

Add $1$ and $1$ .

$5 - 8 i - 4 i + 6 i^{2}$

Simplify each term.

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

$5 - 8 i - 4 i + 6 \cdot - 1$

Multiply $6$ by $- 1$ .

$5 - 8 i - 4 i - 6$

Simplify by adding terms.

Subtract $6$ from $5$ .

$- 1 - 8 i - 4 i$

Subtract $4 i$ from $- 8 i$ .

$- 1 - 12 i$