Simplify (-9-6i)/(-3-2i)

$\frac{- 9 - 6 i}{- 3 - 2 i}$

Multiply the numerator and denominator of $\frac{- 9 - 6 i}{- 3 - 2 i}$ by the conjugate of $- 3 - 2 i$ to make the denominator real.

$\frac{- 9 - 6 i}{- 3 - 2 i} \cdot \frac{- 3 + 2 i}{- 3 + 2 i}$

Multiply.

Combine.

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

Simplify the numerator.

Expand $(- 9 - 6 i) (- 3 + 2 i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $- 9$ by $- 3$ .

$\frac{27 - 9 (2 i) - 6 i \cdot - 3 - 6 i (2 i)}{(- 3 - 2 i) (- 3 + 2 i)}$

Multiply $2$ by $- 9$ .

$\frac{27 - 18 i - 6 i \cdot - 3 - 6 i (2 i)}{(- 3 - 2 i) (- 3 + 2 i)}$

Multiply $- 3$ by $- 6$ .

$\frac{27 - 18 i + 18 i - 6 i (2 i)}{(- 3 - 2 i) (- 3 + 2 i)}$

Multiply $- 6 i (2 i)$ .

Multiply $2$ by $- 6$ .

$\frac{27 - 18 i + 18 i - 12 i i}{(- 3 - 2 i) (- 3 + 2 i)}$

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

$\frac{27 - 18 i + 18 i - 12 (i^{1} i)}{(- 3 - 2 i) (- 3 + 2 i)}$

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

$\frac{27 - 18 i + 18 i - 12 (i^{1} i^{1})}{(- 3 - 2 i) (- 3 + 2 i)}$

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

$\frac{27 - 18 i + 18 i - 12 i^{1 + 1}}{(- 3 - 2 i) (- 3 + 2 i)}$

Add $1$ and $1$ .

$\frac{27 - 18 i + 18 i - 12 i^{2}}{(- 3 - 2 i) (- 3 + 2 i)}$

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

$\frac{27 - 18 i + 18 i - 12 \cdot - 1}{(- 3 - 2 i) (- 3 + 2 i)}$

Multiply $- 12$ by $- 1$ .

$\frac{27 - 18 i + 18 i + 12}{(- 3 - 2 i) (- 3 + 2 i)}$

Add $27$ and $12$ .

$\frac{39 - 18 i + 18 i}{(- 3 - 2 i) (- 3 + 2 i)}$

Add $- 18 i$ and $18 i$ .

$\frac{39 + 0}{(- 3 - 2 i) (- 3 + 2 i)}$

Add $39$ and $0$ .

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

Simplify the denominator.

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify.

Multiply $- 3$ by $- 3$ .

$\frac{39}{9 - 3 (2 i) - 2 i \cdot - 3 - 2 i (2 i)}$

Multiply $2$ by $- 3$ .

$\frac{39}{9 - 6 i - 2 i \cdot - 3 - 2 i (2 i)}$

Multiply $- 3$ by $- 2$ .

$\frac{39}{9 - 6 i + 6 i - 2 i (2 i)}$

Multiply $2$ by $- 2$ .

$\frac{39}{9 - 6 i + 6 i - 4 i i}$

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

$\frac{39}{9 - 6 i + 6 i - 4 (i^{1} i)}$

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

$\frac{39}{9 - 6 i + 6 i - 4 (i^{1} i^{1})}$

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

$\frac{39}{9 - 6 i + 6 i - 4 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{39}{9 - 6 i + 6 i - 4 i^{2}}$

Add $- 6 i$ and $6 i$ .

$\frac{39}{9 + 0 - 4 i^{2}}$

Add $9$ and $0$ .

$\frac{39}{9 - 4 i^{2}}$

Simplify each term.

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

$\frac{39}{9 - 4 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$\frac{39}{9 + 4}$

Add $9$ and $4$ .

$\frac{39}{13}$

Divide $39$ by $13$ .

$3$

Simplify (-9-6i)/(-3-2i)

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