Simplify (-6-4i)/(-5i)

$\frac{- 6 - 4 i}{- 5 i}$

Step 1

Multiply the numerator and denominator of $\frac{- 6 - 4 i}{- 5 i}$ by the conjugate of $- 5 i$ to make the denominator real.

$\frac{- 6 - 4 i}{- 5 i} \cdot \frac{i}{i}$

Step 2

Multiply.

Combine.

$\frac{(- 6 - 4 i) i}{- 5 i i}$

Simplify the numerator.

Apply the distributive property.

$\frac{- 6 i - 4 i i}{- 5 i i}$

Multiply $- 4 i i$ .

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

$\frac{- 6 i - 4 (i^{1} i)}{- 5 i i}$

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

$\frac{- 6 i - 4 (i^{1} i^{1})}{- 5 i i}$

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

$\frac{- 6 i - 4 i^{1 + 1}}{- 5 i i}$

Add $1$ and $1$ .

$\frac{- 6 i - 4 i^{2}}{- 5 i i}$

Simplify each term.

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

$\frac{- 6 i - 4 \cdot - 1}{- 5 i i}$

Multiply $- 4$ by $- 1$ .

$\frac{- 6 i + 4}{- 5 i i}$

Reorder $- 6 i$ and $4$ .

$\frac{4 - 6 i}{- 5 i i}$

Simplify the denominator.

Add parentheses.

$\frac{4 - 6 i}{- 5 (i i)}$

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

$\frac{4 - 6 i}{- 5 (i^{1} i)}$

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

$\frac{4 - 6 i}{- 5 (i^{1} i^{1})}$

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

$\frac{4 - 6 i}{- 5 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{4 - 6 i}{- 5 i^{2}}$

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

$\frac{4 - 6 i}{- 5 \cdot - 1}$

Step 3

Multiply $- 5$ by $- 1$ .

$\frac{4 - 6 i}{5}$

Step 4

Split the fraction $\frac{4 - 6 i}{5}$ into two fractions.

$\frac{4}{5} + \frac{- 6 i}{5}$

Step 5

Move the negative in front of the fraction.

$\frac{4}{5} - \frac{6 i}{5}$

Simplify (-6-4i)/(-5i)

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