Write in Standard Form (2-3i)+5i(1-3i)

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

Simplify each term.

Apply the distributive property.

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

Multiply $5$ by $1$ .

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

Multiply $5 i (- 3 i)$ .

Multiply $- 3$ by $5$ .

$2 - 3 i + 5 i - 15 i i$

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

$2 - 3 i + 5 i - 15 (i^{1} i)$

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

$2 - 3 i + 5 i - 15 (i^{1} i^{1})$

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

$2 - 3 i + 5 i - 15 i^{1 + 1}$

Add $1$ and $1$ .

$2 - 3 i + 5 i - 15 i^{2}$

Simplify each term.

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

$2 - 3 i + 5 i - 15 \cdot - 1$

Multiply $- 15$ by $- 1$ .

$2 - 3 i + 5 i + 15$

Simplify by adding terms.

Add $2$ and $15$ .

$17 - 3 i + 5 i$

Add $- 3 i$ and $5 i$ .

$17 + 2 i$