Simplify -2i(4-3i)+6i

$- 2 i (4 - 3 i) + 6 i$

Step 1

Simplify each term.

Apply the distributive property.

$- 2 i \cdot 4 - 2 i (- 3 i) + 6 i$

Multiply $4$ by $- 2$ .

$- 8 i - 2 i (- 3 i) + 6 i$

Multiply $- 2 i (- 3 i)$ .

Multiply $- 3$ by $- 2$ .

$- 8 i + 6 i i + 6 i$

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

$- 8 i + 6 (i^{1} i) + 6 i$

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

$- 8 i + 6 (i^{1} i^{1}) + 6 i$

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

$- 8 i + 6 i^{1 + 1} + 6 i$

Add $1$ and $1$ .

$- 8 i + 6 i^{2} + 6 i$

Simplify each term.

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

$- 8 i + 6 \cdot - 1 + 6 i$

Multiply $6$ by $- 1$ .

$- 8 i - 6 + 6 i$

Step 2

Add $- 8 i$ and $6 i$ .

$- 6 - 2 i$