Simplify (6-6i)/(-4i)

$\frac{6 - 6 i}{- 4 i}$

Step 1

Cancel the common factor of $6 - 6 i$ and $- 4$ .

Factor $2$ out of $6$ .

$\frac{2 (3) - 6 i}{- 4 i}$

Factor $2$ out of $- 6 i$ .

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

Factor $2$ out of $2 (3) + 2 (- 3 i)$ .

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

Cancel the common factors.

Factor $2$ out of $- 4 i$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 - 3 i}{- 2 i}$

Step 2

Multiply the numerator and denominator of $\frac{3 - 3 i}{- 2 i}$ by the conjugate of $- 2 i$ to make the denominator real.

$\frac{3 - 3 i}{- 2 i} \cdot \frac{i}{i}$

Step 3

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

$\frac{3 i - 3 i i}{- 2 i i}$

Multiply $- 3 i i$ .

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

$\frac{3 i - 3 (i^{1} i)}{- 2 i i}$

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

$\frac{3 i - 3 (i^{1} i^{1})}{- 2 i i}$

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

$\frac{3 i - 3 i^{1 + 1}}{- 2 i i}$

Add $1$ and $1$ .

$\frac{3 i - 3 i^{2}}{- 2 i i}$

Simplify each term.

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

$\frac{3 i - 3 \cdot - 1}{- 2 i i}$

Multiply $- 3$ by $- 1$ .

$\frac{3 i + 3}{- 2 i i}$

Reorder $3 i$ and $3$ .

$\frac{3 + 3 i}{- 2 i i}$

Simplify the denominator.

Add parentheses.

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

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

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

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

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

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

$\frac{3 + 3 i}{- 2 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{3 + 3 i}{- 2 i^{2}}$

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

$\frac{3 + 3 i}{- 2 \cdot - 1}$

Step 4

Multiply $- 2$ by $- 1$ .

$\frac{3 + 3 i}{2}$

Step 5

Split the fraction $\frac{3 + 3 i}{2}$ into two fractions.

$\frac{3}{2} + \frac{3 i}{2}$

Simplify (6-6i)/(-4i)

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