Divide (-10+14i)/(-11+11i)

$\frac{- 10 + 14 i}{- 11 + 11 i}$

Multiply the numerator and denominator of $\frac{- 10 + 14 i}{- 11 + 11 i}$ by the conjugate of $- 11 + 11 i$ to make the denominator real.

$\frac{- 10 + 14 i}{- 11 + 11 i} \cdot \frac{- 11 - 11 i}{- 11 - 11 i}$

Multiply.

Combine.

$\frac{(- 10 + 14 i) (- 11 - 11 i)}{(- 11 + 11 i) (- 11 - 11 i)}$

Simplify the numerator.

Expand $(- 10 + 14 i) (- 11 - 11 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{- 10 (- 11 - 11 i) + 14 i (- 11 - 11 i)}{(- 11 + 11 i) (- 11 - 11 i)}$

Apply the distributive property.

$\frac{- 10 \cdot - 11 - 10 (- 11 i) + 14 i (- 11 - 11 i)}{(- 11 + 11 i) (- 11 - 11 i)}$

Apply the distributive property.

$\frac{- 10 \cdot - 11 - 10 (- 11 i) + 14 i \cdot - 11 + 14 i (- 11 i)}{(- 11 + 11 i) (- 11 - 11 i)}$

Simplify and combine like terms.

Simplify each term.

Multiply $- 10$ by $- 11$ .

$\frac{110 - 10 (- 11 i) + 14 i \cdot - 11 + 14 i (- 11 i)}{(- 11 + 11 i) (- 11 - 11 i)}$

Multiply $- 11$ by $- 10$ .

$\frac{110 + 110 i + 14 i \cdot - 11 + 14 i (- 11 i)}{(- 11 + 11 i) (- 11 - 11 i)}$

Multiply $- 11$ by $14$ .

$\frac{110 + 110 i - 154 i + 14 i (- 11 i)}{(- 11 + 11 i) (- 11 - 11 i)}$

Multiply $14 i (- 11 i)$ .

Multiply $- 11$ by $14$ .

$\frac{110 + 110 i - 154 i - 154 i i}{(- 11 + 11 i) (- 11 - 11 i)}$

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

$\frac{110 + 110 i - 154 i - 154 (i^{1} i)}{(- 11 + 11 i) (- 11 - 11 i)}$

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

$\frac{110 + 110 i - 154 i - 154 (i^{1} i^{1})}{(- 11 + 11 i) (- 11 - 11 i)}$

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

$\frac{110 + 110 i - 154 i - 154 i^{1 + 1}}{(- 11 + 11 i) (- 11 - 11 i)}$

Add $1$ and $1$ .

$\frac{110 + 110 i - 154 i - 154 i^{2}}{(- 11 + 11 i) (- 11 - 11 i)}$

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

$\frac{110 + 110 i - 154 i - 154 \cdot - 1}{(- 11 + 11 i) (- 11 - 11 i)}$

Multiply $- 154$ by $- 1$ .

$\frac{110 + 110 i - 154 i + 154}{(- 11 + 11 i) (- 11 - 11 i)}$

Add $110$ and $154$ .

$\frac{264 + 110 i - 154 i}{(- 11 + 11 i) (- 11 - 11 i)}$

Subtract $154 i$ from $110 i$ .

$\frac{264 - 44 i}{(- 11 + 11 i) (- 11 - 11 i)}$

Simplify the denominator.

Expand $(- 11 + 11 i) (- 11 - 11 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{264 - 44 i}{- 11 (- 11 - 11 i) + 11 i (- 11 - 11 i)}$

Apply the distributive property.

$\frac{264 - 44 i}{- 11 \cdot - 11 - 11 (- 11 i) + 11 i (- 11 - 11 i)}$

Apply the distributive property.

$\frac{264 - 44 i}{- 11 \cdot - 11 - 11 (- 11 i) + 11 i \cdot - 11 + 11 i (- 11 i)}$

Simplify.

Multiply $- 11$ by $- 11$ .

$\frac{264 - 44 i}{121 - 11 (- 11 i) + 11 i \cdot - 11 + 11 i (- 11 i)}$

Multiply $- 11$ by $- 11$ .

$\frac{264 - 44 i}{121 + 121 i + 11 i \cdot - 11 + 11 i (- 11 i)}$

Multiply $- 11$ by $11$ .

$\frac{264 - 44 i}{121 + 121 i - 121 i + 11 i (- 11 i)}$

Multiply $- 11$ by $11$ .

$\frac{264 - 44 i}{121 + 121 i - 121 i - 121 i i}$

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

$\frac{264 - 44 i}{121 + 121 i - 121 i - 121 (i^{1} i)}$

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

$\frac{264 - 44 i}{121 + 121 i - 121 i - 121 (i^{1} i^{1})}$

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

$\frac{264 - 44 i}{121 + 121 i - 121 i - 121 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{264 - 44 i}{121 + 121 i - 121 i - 121 i^{2}}$

Subtract $121 i$ from $121 i$ .

$\frac{264 - 44 i}{121 + 0 - 121 i^{2}}$

Add $121$ and $0$ .

$\frac{264 - 44 i}{121 - 121 i^{2}}$

Simplify each term.

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

$\frac{264 - 44 i}{121 - 121 \cdot - 1}$

Multiply $- 121$ by $- 1$ .

$\frac{264 - 44 i}{121 + 121}$

Add $121$ and $121$ .

$\frac{264 - 44 i}{242}$

Cancel the common factor of $264 - 44 i$ and $242$ .

Factor $22$ out of $264$ .

$\frac{22 (12) - 44 i}{242}$

Factor $22$ out of $- 44 i$ .

$\frac{22 (12) + 22 (- 2 i)}{242}$

Factor $22$ out of $22 (12) + 22 (- 2 i)$ .

$\frac{22 (12 - 2 i)}{242}$

Cancel the common factors.

Factor $22$ out of $242$ .

$\frac{22 (12 - 2 i)}{22 \cdot 11}$

Cancel the common factor.

$\frac{22 (12 - 2 i)}{22 \cdot 11}$

Rewrite the expression.

$\frac{12 - 2 i}{11}$

Split the fraction $\frac{12 - 2 i}{11}$ into two fractions.

$\frac{12}{11} + \frac{- 2 i}{11}$

Move the negative in front of the fraction.

$\frac{12}{11} - \frac{2 i}{11}$

Divide (-10+14i)/(-11+11i)

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