Simplify 3i(4-i)

$3 i (4 - i)$

Step 1

Apply the distributive property.

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

Step 2

Multiply $4$ by $3$ .

$12 i + 3 i (- i)$

Step 3

Multiply $3 i (- i)$ .

Multiply $- 1$ by $3$ .

$12 i - 3 i i$

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

$12 i - 3 (i^{1} i)$

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

$12 i - 3 (i^{1} i^{1})$

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

$12 i - 3 i^{1 + 1}$

Add $1$ and $1$ .

$12 i - 3 i^{2}$

Step 4

Simplify each term.

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

$12 i - 3 \cdot - 1$

Multiply $- 3$ by $- 1$ .

$12 i + 3$

Step 5

Reorder $12 i$ and $3$ .

$3 + 12 i$