Divide (4+4i)/(-2-8i)

$\frac{4 + 4 i}{- 2 - 8 i}$

Cancel the common factor of $4 + 4 i$ and $- 2 - 8 i$ .

Factor $2$ out of $4$ .

$\frac{2 (2) + 4 i}{- 2 - 8 i}$

Factor $2$ out of $4 i$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $- 2$ .

$\frac{2 (2 + 2 i)}{2 \cdot - 1 - 8 i}$

Factor $2$ out of $- 8 i$ .

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

Factor $2$ out of $2 (- 1) + 2 (- 4 i)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply the numerator and denominator of $\frac{2 + 2 i}{- 1 - 4 i}$ by the conjugate of $- 1 - 4 i$ to make the denominator real.

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

Multiply.

Combine.

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

Simplify the numerator.

Expand $(2 + 2 i) (- 1 + 4 i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $- 1$ .

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

Multiply $4$ by $2$ .

$\frac{- 2 + 8 i + 2 i \cdot - 1 + 2 i (4 i)}{(- 1 - 4 i) (- 1 + 4 i)}$

Multiply $- 1$ by $2$ .

$\frac{- 2 + 8 i - 2 i + 2 i (4 i)}{(- 1 - 4 i) (- 1 + 4 i)}$

Multiply $2 i (4 i)$ .

Multiply $4$ by $2$ .

$\frac{- 2 + 8 i - 2 i + 8 i i}{(- 1 - 4 i) (- 1 + 4 i)}$

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

$\frac{- 2 + 8 i - 2 i + 8 (i^{1} i)}{(- 1 - 4 i) (- 1 + 4 i)}$

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

$\frac{- 2 + 8 i - 2 i + 8 (i^{1} i^{1})}{(- 1 - 4 i) (- 1 + 4 i)}$

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

$\frac{- 2 + 8 i - 2 i + 8 i^{1 + 1}}{(- 1 - 4 i) (- 1 + 4 i)}$

Add $1$ and $1$ .

$\frac{- 2 + 8 i - 2 i + 8 i^{2}}{(- 1 - 4 i) (- 1 + 4 i)}$

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

$\frac{- 2 + 8 i - 2 i + 8 \cdot - 1}{(- 1 - 4 i) (- 1 + 4 i)}$

Multiply $8$ by $- 1$ .

$\frac{- 2 + 8 i - 2 i - 8}{(- 1 - 4 i) (- 1 + 4 i)}$

Subtract $8$ from $- 2$ .

$\frac{- 10 + 8 i - 2 i}{(- 1 - 4 i) (- 1 + 4 i)}$

Subtract $2 i$ from $8 i$ .

$\frac{- 10 + 6 i}{(- 1 - 4 i) (- 1 + 4 i)}$

Simplify the denominator.

Expand $(- 1 - 4 i) (- 1 + 4 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{- 10 + 6 i}{- 1 (- 1 + 4 i) - 4 i (- 1 + 4 i)}$

Apply the distributive property.

$\frac{- 10 + 6 i}{- 1 \cdot - 1 - 1 (4 i) - 4 i (- 1 + 4 i)}$

Apply the distributive property.

$\frac{- 10 + 6 i}{- 1 \cdot - 1 - 1 (4 i) - 4 i \cdot - 1 - 4 i (4 i)}$

Simplify.

Multiply $- 1$ by $- 1$ .

$\frac{- 10 + 6 i}{1 - 1 (4 i) - 4 i \cdot - 1 - 4 i (4 i)}$

Multiply $4$ by $- 1$ .

$\frac{- 10 + 6 i}{1 - 4 i - 4 i \cdot - 1 - 4 i (4 i)}$

Multiply $- 1$ by $- 4$ .

$\frac{- 10 + 6 i}{1 - 4 i + 4 i - 4 i (4 i)}$

Multiply $4$ by $- 4$ .

$\frac{- 10 + 6 i}{1 - 4 i + 4 i - 16 i i}$

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

$\frac{- 10 + 6 i}{1 - 4 i + 4 i - 16 (i^{1} i)}$

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

$\frac{- 10 + 6 i}{1 - 4 i + 4 i - 16 (i^{1} i^{1})}$

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

$\frac{- 10 + 6 i}{1 - 4 i + 4 i - 16 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 10 + 6 i}{1 - 4 i + 4 i - 16 i^{2}}$

Add $- 4 i$ and $4 i$ .

$\frac{- 10 + 6 i}{1 + 0 - 16 i^{2}}$

Add $1$ and $0$ .

$\frac{- 10 + 6 i}{1 - 16 i^{2}}$

Simplify each term.

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

$\frac{- 10 + 6 i}{1 - 16 \cdot - 1}$

Multiply $- 16$ by $- 1$ .

$\frac{- 10 + 6 i}{1 + 16}$

Add $1$ and $16$ .

$\frac{- 10 + 6 i}{17}$

Split the fraction $\frac{- 10 + 6 i}{17}$ into two fractions.

$\frac{- 10}{17} + \frac{6 i}{17}$

Move the negative in front of the fraction.

$- \frac{10}{17} + \frac{6 i}{17}$

Divide (4+4i)/(-2-8i)

Related Questions

Support LCMGCF.com by disabling your adblocker.