Simplify 6i(2-3i)

$6 i (2 - 3 i)$

Step 1

Apply the distributive property.

$6 i \cdot 2 + 6 i (- 3 i)$

Step 2

Multiply $2$ by $6$ .

$12 i + 6 i (- 3 i)$

Step 3

Multiply $6 i (- 3 i)$ .

Multiply $- 3$ by $6$ .

$12 i - 18 i i$

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

$12 i - 18 (i^{1} i)$

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

$12 i - 18 (i^{1} i^{1})$

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

$12 i - 18 i^{1 + 1}$

Add $1$ and $1$ .

$12 i - 18 i^{2}$

Step 4

Simplify each term.

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

$12 i - 18 \cdot - 1$

Multiply $- 18$ by $- 1$ .

$12 i + 18$

Step 5

Reorder $12 i$ and $18$ .

$18 + 12 i$