Divide (12i)/(3-3i)

$\frac{12 i}{3 - 3 i}$

Step 1

Cancel the common factor of $12$ and $3 - 3 i$ .

Factor $3$ out of $12 i$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (4 i)}{3 (1) - 3 i}$

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

$\frac{3 (4 i)}{3 (1) + 3 (- i)}$

Factor $3$ out of $3 (1) + 3 (- i)$ .

$\frac{3 (4 i)}{3 (1 - i)}$

Cancel the common factor.

$\frac{3 (4 i)}{3 (1 - i)}$

Rewrite the expression.

$\frac{4 i}{1 - i}$

Step 2

Multiply the numerator and denominator of $\frac{4 i}{1 - i}$ by the conjugate of $1 - i$ to make the denominator real.

$\frac{4 i}{1 - i} \cdot \frac{1 + i}{1 + i}$

Step 3

Multiply.

Combine.

$\frac{4 i (1 + i)}{(1 - i) (1 + i)}$

Simplify the numerator.

Apply the distributive property.

$\frac{4 i \cdot 1 + 4 i i}{(1 - i) (1 + i)}$

Multiply $4$ by $1$ .

$\frac{4 i + 4 i i}{(1 - i) (1 + i)}$

Multiply $4 i i$ .

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

$\frac{4 i + 4 (i^{1} i)}{(1 - i) (1 + i)}$

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

$\frac{4 i + 4 (i^{1} i^{1})}{(1 - i) (1 + i)}$

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

$\frac{4 i + 4 i^{1 + 1}}{(1 - i) (1 + i)}$

Add $1$ and $1$ .

$\frac{4 i + 4 i^{2}}{(1 - i) (1 + i)}$

Simplify each term.

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

$\frac{4 i + 4 \cdot - 1}{(1 - i) (1 + i)}$

Multiply $4$ by $- 1$ .

$\frac{4 i - 4}{(1 - i) (1 + i)}$

Reorder $4 i$ and $- 4$ .

$\frac{- 4 + 4 i}{(1 - i) (1 + i)}$

Simplify the denominator.

Expand $(1 - i) (1 + i)$ using the FOIL Method.

Apply the distributive property.

$\frac{- 4 + 4 i}{1 (1 + i) - i (1 + i)}$

Apply the distributive property.

$\frac{- 4 + 4 i}{1 \cdot 1 + 1 i - i (1 + i)}$

Apply the distributive property.

$\frac{- 4 + 4 i}{1 \cdot 1 + 1 i - i \cdot 1 - i i}$

Simplify.

Multiply $1$ by $1$ .

$\frac{- 4 + 4 i}{1 + 1 i - i \cdot 1 - i i}$

Multiply $- 1$ by $1$ .

$\frac{- 4 + 4 i}{1 + 1 i - i - i i}$

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

$\frac{- 4 + 4 i}{1 + 1 i - i - (i^{1} i)}$

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

$\frac{- 4 + 4 i}{1 + 1 i - i - (i^{1} i^{1})}$

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

$\frac{- 4 + 4 i}{1 + 1 i - i - i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 4 + 4 i}{1 + 1 i - i - i^{2}}$

Subtract $i$ from $1 i$ .

$\frac{- 4 + 4 i}{1 + 0 - i^{2}}$

Add $1$ and $0$ .

$\frac{- 4 + 4 i}{1 - i^{2}}$

Simplify each term.

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

$\frac{- 4 + 4 i}{1 - - 1}$

Multiply $- 1$ by $- 1$ .

$\frac{- 4 + 4 i}{1 + 1}$

Add $1$ and $1$ .

$\frac{- 4 + 4 i}{2}$

Step 4

Cancel the common factor of $- 4 + 4 i$ and $2$ .

Factor $2$ out of $- 4$ .

$\frac{2 \cdot - 2 + 4 i}{2}$

Factor $2$ out of $4 i$ .

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

Factor $2$ out of $2 (- 2) + 2 (2 i)$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 2 + 2 i}{1}$

Divide $- 2 + 2 i$ by $1$ .

$- 2 + 2 i$

Divide (12i)/(3-3i)

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