Simplify 1/3(6+3i)-2/3(6-12i)

$\frac{1}{3} (6 + 3 i) - \frac{2}{3} (6 - 12 i)$

Step 1

Simplify each term.

Apply the distributive property.

$\frac{1}{3} \cdot 6 + \frac{1}{3} (3 i) - \frac{2}{3} \cdot (6 - 12 i)$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{1}{3} \cdot (3 (2)) + \frac{1}{3} (3 i) - \frac{2}{3} \cdot (6 - 12 i)$

Cancel the common factor.

$\frac{1}{3} \cdot (3 \cdot 2) + \frac{1}{3} (3 i) - \frac{2}{3} \cdot (6 - 12 i)$

Rewrite the expression.

$2 + \frac{1}{3} (3 i) - \frac{2}{3} \cdot (6 - 12 i)$

Cancel the common factor of $3$ .

Factor $3$ out of $3 i$ .

$2 + \frac{1}{3} (3 (i)) - \frac{2}{3} \cdot (6 - 12 i)$

Cancel the common factor.

$2 + \frac{1}{3} (3 i) - \frac{2}{3} \cdot (6 - 12 i)$

Rewrite the expression.

$2 + i - \frac{2}{3} \cdot (6 - 12 i)$

Apply the distributive property.

$2 + i - \frac{2}{3} \cdot 6 - \frac{2}{3} (- 12 i)$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$2 + i + \frac{- 2}{3} \cdot 6 - \frac{2}{3} (- 12 i)$

Factor $3$ out of $6$ .

$2 + i + \frac{- 2}{3} \cdot (3 (2)) - \frac{2}{3} (- 12 i)$

Cancel the common factor.

$2 + i + \frac{- 2}{3} \cdot (3 \cdot 2) - \frac{2}{3} (- 12 i)$

Rewrite the expression.

$2 + i - 2 \cdot 2 - \frac{2}{3} (- 12 i)$

Multiply $- 2$ by $2$ .

$2 + i - 4 - \frac{2}{3} (- 12 i)$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$2 + i - 4 + \frac{- 2}{3} (- 12 i)$

Factor $3$ out of $- 12 i$ .

$2 + i - 4 + \frac{- 2}{3} (3 (- 4 i))$

Cancel the common factor.

$2 + i - 4 + \frac{- 2}{3} (3 (- 4 i))$

Rewrite the expression.

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

Multiply $- 4$ by $- 2$ .

$2 + i - 4 + 8 i$

Step 2

Simplify by adding terms.

Subtract $4$ from $2$ .

$- 2 + i + 8 i$

Add $i$ and $8 i$ .

$- 2 + 9 i$

Simplify 1/3(6+3i)-2/3(6-12i)

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