Write in Standard Form (-7+i)/(-1-i)

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

Step 1

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

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

Step 2

Multiply.

Combine.

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

Simplify the numerator.

Expand $(- 7 + i) (- 1 + i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $- 7$ by $- 1$ .

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

Move $- 1$ to the left of $i$ .

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

Rewrite $- 1 i$ as $- i$ .

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

Multiply $i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Subtract $1$ from $7$ .

$\frac{6 - 7 i - i}{(- 1 - i) (- 1 + i)}$

Subtract $i$ from $- 7 i$ .

$\frac{6 - 8 i}{(- 1 - i) (- 1 + i)}$

Simplify the denominator.

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

Apply the distributive property.

$\frac{6 - 8 i}{- 1 (- 1 + i) - i (- 1 + i)}$

Apply the distributive property.

$\frac{6 - 8 i}{- 1 \cdot - 1 - 1 i - i (- 1 + i)}$

Apply the distributive property.

$\frac{6 - 8 i}{- 1 \cdot - 1 - 1 i - i \cdot - 1 - i i}$

Simplify.

Multiply $- 1$ by $- 1$ .

$\frac{6 - 8 i}{1 - 1 i - i \cdot - 1 - i i}$

Multiply $- 1$ by $- 1$ .

$\frac{6 - 8 i}{1 - 1 i + 1 i - i i}$

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

$\frac{6 - 8 i}{1 - 1 i + 1 i - (i^{1} i)}$

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

$\frac{6 - 8 i}{1 - 1 i + 1 i - (i^{1} i^{1})}$

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

$\frac{6 - 8 i}{1 - 1 i + 1 i - i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{6 - 8 i}{1 - 1 i + 1 i - i^{2}}$

Add $- 1 i$ and $1 i$ .

$\frac{6 - 8 i}{1 + 0 - i^{2}}$

Add $1$ and $0$ .

$\frac{6 - 8 i}{1 - i^{2}}$

Simplify each term.

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

$\frac{6 - 8 i}{1 - - 1}$

Multiply $- 1$ by $- 1$ .

$\frac{6 - 8 i}{1 + 1}$

Add $1$ and $1$ .

$\frac{6 - 8 i}{2}$

Step 3

Cancel the common factor of $6 - 8 i$ and $2$ .

Factor $2$ out of $6$ .

$\frac{2 \cdot 3 - 8 i}{2}$

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

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

Factor $2$ out of $2 (3) + 2 (- 4 i)$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (3 - 4 i)}{2 (1)}$

Cancel the common factor.

$\frac{2 (3 - 4 i)}{2 \cdot 1}$

Rewrite the expression.

$\frac{3 - 4 i}{1}$

Divide $3 - 4 i$ by $1$ .

$3 - 4 i$

Write in Standard Form (-7+i)/(-1-i)

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