Write in Standard Form (5+30i)/(-6i)

$\frac{5 + 30 i}{- 6 i}$

Step 1

Multiply the numerator and denominator of $\frac{5 + 30 i}{- 6 i}$ by the conjugate of $- 6 i$ to make the denominator real.

$\frac{5 + 30 i}{- 6 i} \cdot \frac{i}{i}$

Step 2

Multiply.

Combine.

$\frac{(5 + 30 i) i}{- 6 i i}$

Simplify the numerator.

Apply the distributive property.

$\frac{5 i + 30 i i}{- 6 i i}$

Multiply $30 i i$ .

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

$\frac{5 i + 30 (i^{1} i)}{- 6 i i}$

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

$\frac{5 i + 30 (i^{1} i^{1})}{- 6 i i}$

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

$\frac{5 i + 30 i^{1 + 1}}{- 6 i i}$

Add $1$ and $1$ .

$\frac{5 i + 30 i^{2}}{- 6 i i}$

Simplify each term.

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

$\frac{5 i + 30 \cdot - 1}{- 6 i i}$

Multiply $30$ by $- 1$ .

$\frac{5 i - 30}{- 6 i i}$

Reorder $5 i$ and $- 30$ .

$\frac{- 30 + 5 i}{- 6 i i}$

Simplify the denominator.

Add parentheses.

$\frac{- 30 + 5 i}{- 6 (i i)}$

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

$\frac{- 30 + 5 i}{- 6 (i^{1} i)}$

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

$\frac{- 30 + 5 i}{- 6 (i^{1} i^{1})}$

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

$\frac{- 30 + 5 i}{- 6 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 30 + 5 i}{- 6 i^{2}}$

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

$\frac{- 30 + 5 i}{- 6 \cdot - 1}$

Step 3

Multiply $- 6$ by $- 1$ .

$\frac{- 30 + 5 i}{6}$

Step 4

Split the fraction $\frac{- 30 + 5 i}{6}$ into two fractions.

$\frac{- 30}{6} + \frac{5 i}{6}$

Step 5

Divide $- 30$ by $6$ .

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

Write in Standard Form (5+30i)/(-6i)

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