Simplify (-1+8i)/(-i)

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

Step 1

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

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

Step 2

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

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

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

Multiply $8 i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

Simplify each term.

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

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

Multiply $8$ by $- 1$ .

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

Reorder $- i$ and $- 8$ .

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

Simplify the denominator.

Add parentheses.

$\frac{- 8 - i}{- (i i)}$

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Step 3

Multiply $- 1$ by $- 1$ .

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

Step 4

Divide $- 8 - i$ by $1$ .

$- 8 - i$

Simplify (-1+8i)/(-i)

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