Simplify 4i(3-5i)

$4 i (3 - 5 i)$

Step 1

Apply the distributive property.

$4 i \cdot 3 + 4 i (- 5 i)$

Step 2

Multiply $3$ by $4$ .

$12 i + 4 i (- 5 i)$

Step 3

Multiply $4 i (- 5 i)$ .

Multiply $- 5$ by $4$ .

$12 i - 20 i i$

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

$12 i - 20 (i^{1} i)$

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

$12 i - 20 (i^{1} i^{1})$

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

$12 i - 20 i^{1 + 1}$

Add $1$ and $1$ .

$12 i - 20 i^{2}$

Step 4

Simplify each term.

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

$12 i - 20 \cdot - 1$

Multiply $- 20$ by $- 1$ .

$12 i + 20$

Step 5

Reorder $12 i$ and $20$ .

$20 + 12 i$