Simplify 5i(3-2i)

$5 i (3 - 2 i)$

Step 1

Apply the distributive property.

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

Step 2

Multiply $3$ by $5$ .

$15 i + 5 i (- 2 i)$

Step 3

Multiply $5 i (- 2 i)$ .

Multiply $- 2$ by $5$ .

$15 i - 10 i i$

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

$15 i - 10 (i^{1} i)$

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

$15 i - 10 (i^{1} i^{1})$

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

$15 i - 10 i^{1 + 1}$

Add $1$ and $1$ .

$15 i - 10 i^{2}$

Step 4

Simplify each term.

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

$15 i - 10 \cdot - 1$

Multiply $- 10$ by $- 1$ .

$15 i + 10$

Step 5

Reorder $15 i$ and $10$ .

$10 + 15 i$