Precalculus Examples

$\frac{- 4 + 8 i}{- 6 i}$

Step 1

Cancel the common factor of $- 4 + 8 i$ and $- 6$ .

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Step 1.1

Factor $2$ out of $- 4$ .

$\frac{2 (- 2) + 8 i}{- 6 i}$

Step 1.2

Factor $2$ out of $8 i$ .

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

Step 1.3

Factor $2$ out of $2 (- 2) + 2 (4 i)$ .

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

Step 1.4

Cancel the common factors.

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Step 1.4.1

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

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 2

Multiply the numerator and denominator of $\frac{- 2 + 4 i}{- 3 i}$ by the conjugate of $- 3 i$ to make the denominator real.

$\frac{- 2 + 4 i}{- 3 i} \cdot \frac{i}{i}$

Step 3

Multiply.

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Step 3.1

Combine.

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

Step 3.2

Simplify the numerator.

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Step 3.2.1

Apply the distributive property.

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

Step 3.2.2

Multiply $4 i i$ .

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Step 3.2.2.1

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

$\frac{- 2 i + 4 (i^{1} i)}{- 3 i i}$

Step 3.2.2.2

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

$\frac{- 2 i + 4 (i^{1} i^{1})}{- 3 i i}$

Step 3.2.2.3

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

$\frac{- 2 i + 4 i^{1 + 1}}{- 3 i i}$

Step 3.2.2.4

Add $1$ and $1$ .

$\frac{- 2 i + 4 i^{2}}{- 3 i i}$

Step 3.2.3

Simplify each term.

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Step 3.2.3.1

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

$\frac{- 2 i + 4 \cdot - 1}{- 3 i i}$

Step 3.2.3.2

Multiply $4$ by $- 1$ .

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

Step 3.2.4

Reorder $- 2 i$ and $- 4$ .

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

Step 3.3

Simplify the denominator.

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Step 3.3.1

Add parentheses.

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

Step 3.3.2

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

$\frac{- 4 - 2 i}{- 3 (i^{1} i)}$

Step 3.3.3

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

$\frac{- 4 - 2 i}{- 3 (i^{1} i^{1})}$

Step 3.3.4

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

$\frac{- 4 - 2 i}{- 3 i^{1 + 1}}$

Step 3.3.5

Add $1$ and $1$ .

$\frac{- 4 - 2 i}{- 3 i^{2}}$

Step 3.3.6

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

$\frac{- 4 - 2 i}{- 3 \cdot - 1}$

Step 4

Multiply $- 3$ by $- 1$ .

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

Step 5

Split the fraction $\frac{- 4 - 2 i}{3}$ into two fractions.

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

Step 6

Simplify each term.

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Step 6.1

Move the negative in front of the fraction.

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

Step 6.2

Move the negative in front of the fraction.

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