Simplify (-1+i)/(-6i)

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

Multiply the numerator and denominator of $\frac{- 1 + i}{- 6 i}$ by the conjugate of $- 6 i$ to make the denominator real.

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

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

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

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

Multiply $i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Reorder $- i$ and $- 1$ .

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

Simplify the denominator.

Add parentheses.

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $- 6$ by $- 1$ .

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

Split the fraction $\frac{- 1 - i}{6}$ into two fractions.

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

Simplify each term.

Move the negative in front of the fraction.

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

Move the negative in front of the fraction.

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

Simplify (-1+i)/(-6i)

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