Evaluate (-7-i)/(-8+i)

$\frac{- 7 - i}{- 8 + i}$

Step 1

Multiply the numerator and denominator of $\frac{- 7 - i}{- 8 + 1 i}$ by the conjugate of $- 8 + 1 i$ to make the denominator real.

$\frac{- 7 - i}{- 8 + 1 i} \cdot \frac{- 8 - i}{- 8 - i}$

Step 2

Multiply.

Combine.

$\frac{(- 7 - i) (- 8 - i)}{(- 8 + 1 i) (- 8 - i)}$

Simplify the numerator.

Expand $(- 7 - i) (- 8 - i)$ using the FOIL Method.

Apply the distributive property.

$\frac{- 7 (- 8 - i) - i (- 8 - i)}{(- 8 + 1 i) (- 8 - i)}$

Apply the distributive property.

$\frac{- 7 \cdot - 8 - 7 (- i) - i (- 8 - i)}{(- 8 + 1 i) (- 8 - i)}$

Apply the distributive property.

$\frac{- 7 \cdot - 8 - 7 (- i) - i \cdot - 8 - i (- i)}{(- 8 + 1 i) (- 8 - i)}$

Simplify and combine like terms.

Simplify each term.

Multiply $- 7$ by $- 8$ .

$\frac{56 - 7 (- i) - i \cdot - 8 - i (- i)}{(- 8 + 1 i) (- 8 - i)}$

Multiply $- 1$ by $- 7$ .

$\frac{56 + 7 i - i \cdot - 8 - i (- i)}{(- 8 + 1 i) (- 8 - i)}$

Multiply $- 8$ by $- 1$ .

$\frac{56 + 7 i + 8 i - i (- i)}{(- 8 + 1 i) (- 8 - i)}$

Multiply $- i (- i)$ .

Multiply $- 1$ by $- 1$ .

$\frac{56 + 7 i + 8 i + 1 i i}{(- 8 + 1 i) (- 8 - i)}$

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

$\frac{56 + 7 i + 8 i + 1 (i^{1} i)}{(- 8 + 1 i) (- 8 - i)}$

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

$\frac{56 + 7 i + 8 i + 1 (i^{1} i^{1})}{(- 8 + 1 i) (- 8 - i)}$

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

$\frac{56 + 7 i + 8 i + 1 i^{1 + 1}}{(- 8 + 1 i) (- 8 - i)}$

Add $1$ and $1$ .

$\frac{56 + 7 i + 8 i + 1 i^{2}}{(- 8 + 1 i) (- 8 - i)}$

Multiply $i^{2}$ by $1$ .

$\frac{56 + 7 i + 8 i + i^{2}}{(- 8 + 1 i) (- 8 - i)}$

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

$\frac{56 + 7 i + 8 i - 1}{(- 8 + 1 i) (- 8 - i)}$

Subtract $1$ from $56$ .

$\frac{55 + 7 i + 8 i}{(- 8 + 1 i) (- 8 - i)}$

Add $7 i$ and $8 i$ .

$\frac{55 + 15 i}{(- 8 + 1 i) (- 8 - i)}$

Simplify the denominator.

Expand $(- 8 + 1 i) (- 8 - i)$ using the FOIL Method.

Apply the distributive property.

$\frac{55 + 15 i}{- 8 (- 8 - i) + 1 i (- 8 - i)}$

Apply the distributive property.

$\frac{55 + 15 i}{- 8 \cdot - 8 - 8 (- i) + 1 i (- 8 - i)}$

Apply the distributive property.

$\frac{55 + 15 i}{- 8 \cdot - 8 - 8 (- i) + 1 i \cdot - 8 + 1 i (- i)}$

Simplify.

Multiply $- 8$ by $- 8$ .

$\frac{55 + 15 i}{64 - 8 (- i) + 1 i \cdot - 8 + 1 i (- i)}$

Multiply $- 1$ by $- 8$ .

$\frac{55 + 15 i}{64 + 8 i + 1 i \cdot - 8 + 1 i (- i)}$

Multiply $- 8$ by $1$ .

$\frac{55 + 15 i}{64 + 8 i - 8 i + 1 i (- i)}$

Multiply $- 1$ by $1$ .

$\frac{55 + 15 i}{64 + 8 i - 8 i - i i}$

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

$\frac{55 + 15 i}{64 + 8 i - 8 i - (i^{1} i)}$

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

$\frac{55 + 15 i}{64 + 8 i - 8 i - (i^{1} i^{1})}$

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

$\frac{55 + 15 i}{64 + 8 i - 8 i - i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{55 + 15 i}{64 + 8 i - 8 i - i^{2}}$

Subtract $8 i$ from $8 i$ .

$\frac{55 + 15 i}{64 + 0 - i^{2}}$

Add $64$ and $0$ .

$\frac{55 + 15 i}{64 - i^{2}}$

Simplify each term.

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

$\frac{55 + 15 i}{64 - - 1}$

Multiply $- 1$ by $- 1$ .

$\frac{55 + 15 i}{64 + 1}$

Add $64$ and $1$ .

$\frac{55 + 15 i}{65}$

Step 3

Cancel the common factor of $55 + 15 i$ and $65$ .

Factor $5$ out of $55$ .

$\frac{5 (11) + 15 i}{65}$

Factor $5$ out of $15 i$ .

$\frac{5 (11) + 5 (3 i)}{65}$

Factor $5$ out of $5 (11) + 5 (3 i)$ .

$\frac{5 (11 + 3 i)}{65}$

Cancel the common factors.

Factor $5$ out of $65$ .

$\frac{5 (11 + 3 i)}{5 \cdot 13}$

Cancel the common factor.

$\frac{5 (11 + 3 i)}{5 \cdot 13}$

Rewrite the expression.

$\frac{11 + 3 i}{13}$

Step 4

Split the fraction $\frac{11 + 3 i}{13}$ into two fractions.

$\frac{11}{13} + \frac{3 i}{13}$

Evaluate (-7-i)/(-8+i)

Related Questions

Support LCMGCF.com by disabling your adblocker.