Simplify (-26-26i)/(-6+4i)

$\frac{- 26 - 26 i}{- 6 + 4 i}$

Cancel the common factor of $- 26 - 26 i$ and $- 6 + 4 i$ .

Factor $2$ out of $- 26$ .

$\frac{2 (- 13) - 26 i}{- 6 + 4 i}$

Factor $2$ out of $- 26 i$ .

$\frac{2 (- 13) + 2 (- 13 i)}{- 6 + 4 i}$

Factor $2$ out of $2 (- 13) + 2 (- 13 i)$ .

$\frac{2 (- 13 - 13 i)}{- 6 + 4 i}$

Cancel the common factors.

Factor $2$ out of $- 6$ .

$\frac{2 (- 13 - 13 i)}{2 \cdot - 3 + 4 i}$

Factor $2$ out of $4 i$ .

$\frac{2 (- 13 - 13 i)}{2 \cdot - 3 + 2 (2 i)}$

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

$\frac{2 (- 13 - 13 i)}{2 (- 3 + 2 i)}$

Cancel the common factor.

$\frac{2 (- 13 - 13 i)}{2 (- 3 + 2 i)}$

Rewrite the expression.

$\frac{- 13 - 13 i}{- 3 + 2 i}$

Multiply the numerator and denominator of $\frac{- 13 - 13 i}{- 3 + 2 i}$ by the conjugate of $- 3 + 2 i$ to make the denominator real.

$\frac{- 13 - 13 i}{- 3 + 2 i} \cdot \frac{- 3 - 2 i}{- 3 - 2 i}$

Multiply.

Combine.

$\frac{(- 13 - 13 i) (- 3 - 2 i)}{(- 3 + 2 i) (- 3 - 2 i)}$

Simplify the numerator.

Expand $(- 13 - 13 i) (- 3 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{- 13 (- 3 - 2 i) - 13 i (- 3 - 2 i)}{(- 3 + 2 i) (- 3 - 2 i)}$

Apply the distributive property.

$\frac{- 13 \cdot - 3 - 13 (- 2 i) - 13 i (- 3 - 2 i)}{(- 3 + 2 i) (- 3 - 2 i)}$

Apply the distributive property.

$\frac{- 13 \cdot - 3 - 13 (- 2 i) - 13 i \cdot - 3 - 13 i (- 2 i)}{(- 3 + 2 i) (- 3 - 2 i)}$

Simplify and combine like terms.

Simplify each term.

Multiply $- 13$ by $- 3$ .

$\frac{39 - 13 (- 2 i) - 13 i \cdot - 3 - 13 i (- 2 i)}{(- 3 + 2 i) (- 3 - 2 i)}$

Multiply $- 2$ by $- 13$ .

$\frac{39 + 26 i - 13 i \cdot - 3 - 13 i (- 2 i)}{(- 3 + 2 i) (- 3 - 2 i)}$

Multiply $- 3$ by $- 13$ .

$\frac{39 + 26 i + 39 i - 13 i (- 2 i)}{(- 3 + 2 i) (- 3 - 2 i)}$

Multiply $- 13 i (- 2 i)$ .

Multiply $- 2$ by $- 13$ .

$\frac{39 + 26 i + 39 i + 26 i i}{(- 3 + 2 i) (- 3 - 2 i)}$

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

$\frac{39 + 26 i + 39 i + 26 (i^{1} i)}{(- 3 + 2 i) (- 3 - 2 i)}$

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

$\frac{39 + 26 i + 39 i + 26 (i^{1} i^{1})}{(- 3 + 2 i) (- 3 - 2 i)}$

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

$\frac{39 + 26 i + 39 i + 26 i^{1 + 1}}{(- 3 + 2 i) (- 3 - 2 i)}$

Add $1$ and $1$ .

$\frac{39 + 26 i + 39 i + 26 i^{2}}{(- 3 + 2 i) (- 3 - 2 i)}$

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

$\frac{39 + 26 i + 39 i + 26 \cdot - 1}{(- 3 + 2 i) (- 3 - 2 i)}$

Multiply $26$ by $- 1$ .

$\frac{39 + 26 i + 39 i - 26}{(- 3 + 2 i) (- 3 - 2 i)}$

Subtract $26$ from $39$ .

$\frac{13 + 26 i + 39 i}{(- 3 + 2 i) (- 3 - 2 i)}$

Add $26 i$ and $39 i$ .

$\frac{13 + 65 i}{(- 3 + 2 i) (- 3 - 2 i)}$

Simplify the denominator.

Expand $(- 3 + 2 i) (- 3 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{13 + 65 i}{- 3 (- 3 - 2 i) + 2 i (- 3 - 2 i)}$

Apply the distributive property.

$\frac{13 + 65 i}{- 3 \cdot - 3 - 3 (- 2 i) + 2 i (- 3 - 2 i)}$

Apply the distributive property.

$\frac{13 + 65 i}{- 3 \cdot - 3 - 3 (- 2 i) + 2 i \cdot - 3 + 2 i (- 2 i)}$

Simplify.

Multiply $- 3$ by $- 3$ .

$\frac{13 + 65 i}{9 - 3 (- 2 i) + 2 i \cdot - 3 + 2 i (- 2 i)}$

Multiply $- 2$ by $- 3$ .

$\frac{13 + 65 i}{9 + 6 i + 2 i \cdot - 3 + 2 i (- 2 i)}$

Multiply $- 3$ by $2$ .

$\frac{13 + 65 i}{9 + 6 i - 6 i + 2 i (- 2 i)}$

Multiply $- 2$ by $2$ .

$\frac{13 + 65 i}{9 + 6 i - 6 i - 4 i i}$

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

$\frac{13 + 65 i}{9 + 6 i - 6 i - 4 (i^{1} i)}$

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

$\frac{13 + 65 i}{9 + 6 i - 6 i - 4 (i^{1} i^{1})}$

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

$\frac{13 + 65 i}{9 + 6 i - 6 i - 4 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{13 + 65 i}{9 + 6 i - 6 i - 4 i^{2}}$

Subtract $6 i$ from $6 i$ .

$\frac{13 + 65 i}{9 + 0 - 4 i^{2}}$

Add $9$ and $0$ .

$\frac{13 + 65 i}{9 - 4 i^{2}}$

Simplify each term.

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

$\frac{13 + 65 i}{9 - 4 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$\frac{13 + 65 i}{9 + 4}$

Add $9$ and $4$ .

$\frac{13 + 65 i}{13}$

Cancel the common factor of $13 + 65 i$ and $13$ .

Factor $13$ out of $13$ .

$\frac{13 \cdot 1 + 65 i}{13}$

Factor $13$ out of $65 i$ .

$\frac{13 \cdot 1 + 13 (5 i)}{13}$

Factor $13$ out of $13 (1) + 13 (5 i)$ .

$\frac{13 (1 + 5 i)}{13}$

Cancel the common factors.

Factor $13$ out of $13$ .

$\frac{13 (1 + 5 i)}{13 (1)}$

Cancel the common factor.

$\frac{13 (1 + 5 i)}{13 \cdot 1}$

Rewrite the expression.

$\frac{1 + 5 i}{1}$

Divide $1 + 5 i$ by $1$ .

$1 + 5 i$

Simplify (-26-26i)/(-6+4i)

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