Divide (-5-i)/(-10i)

$\frac{- 5 - i}{- 10 i}$

Step 1

Multiply the numerator and denominator of $\frac{- 5 - i}{- 10 i}$ by the conjugate of $- 10 i$ to make the denominator real.

$\frac{- 5 - i}{- 10 i} \cdot \frac{i}{i}$

Step 2

Multiply.

Combine.

$\frac{(- 5 - i) i}{- 10 i i}$

Simplify the numerator.

Apply the distributive property.

$\frac{- 5 i - i i}{- 10 i i}$

Multiply $- i i$ .

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

$\frac{- 5 i - (i^{1} i)}{- 10 i i}$

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

$\frac{- 5 i - (i^{1} i^{1})}{- 10 i i}$

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

$\frac{- 5 i - i^{1 + 1}}{- 10 i i}$

Add $1$ and $1$ .

$\frac{- 5 i - i^{2}}{- 10 i i}$

Simplify each term.

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

$\frac{- 5 i - - 1}{- 10 i i}$

Multiply $- 1$ by $- 1$ .

$\frac{- 5 i + 1}{- 10 i i}$

Reorder $- 5 i$ and $1$ .

$\frac{1 - 5 i}{- 10 i i}$

Simplify the denominator.

Add parentheses.

$\frac{1 - 5 i}{- 10 (i i)}$

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

$\frac{1 - 5 i}{- 10 (i^{1} i)}$

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

$\frac{1 - 5 i}{- 10 (i^{1} i^{1})}$

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

$\frac{1 - 5 i}{- 10 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{1 - 5 i}{- 10 i^{2}}$

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

$\frac{1 - 5 i}{- 10 \cdot - 1}$

Step 3

Multiply $- 10$ by $- 1$ .

$\frac{1 - 5 i}{10}$

Step 4

Split the fraction $\frac{1 - 5 i}{10}$ into two fractions.

$\frac{1}{10} + \frac{- 5 i}{10}$

Step 5

Simplify each term.

Cancel the common factor of $- 5$ and $10$ .

Factor $5$ out of $- 5 i$ .

$\frac{1}{10} + \frac{5 (- i)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{1}{10} + \frac{5 (- i)}{5 (2)}$

Cancel the common factor.

$\frac{1}{10} + \frac{5 (- i)}{5 \cdot 2}$

Rewrite the expression.

$\frac{1}{10} + \frac{- i}{2}$

Move the negative in front of the fraction.

$\frac{1}{10} - \frac{i}{2}$

Divide (-5-i)/(-10i)

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