Precalculus Examples

$\frac{2 + 6 i}{5 i}$

Step 1

Multiply the numerator and denominator of $\frac{2 + 6 i}{5 i}$ by the conjugate of $5 i$ to make the denominator real.

$\frac{2 + 6 i}{5 i} \cdot \frac{i}{i}$

Step 2

Multiply.

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Step 2.1

Combine.

$\frac{(2 + 6 i) i}{5 i i}$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Apply the distributive property.

$\frac{2 i + 6 i i}{5 i i}$

Step 2.2.2

Multiply $6 i i$ .

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Step 2.2.2.1

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

$\frac{2 i + 6 (i^{1} i)}{5 i i}$

Step 2.2.2.2

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

$\frac{2 i + 6 (i^{1} i^{1})}{5 i i}$

Step 2.2.2.3

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

$\frac{2 i + 6 i^{1 + 1}}{5 i i}$

Step 2.2.2.4

Add $1$ and $1$ .

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

Step 2.2.3

Simplify each term.

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Step 2.2.3.1

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

$\frac{2 i + 6 \cdot - 1}{5 i i}$

Step 2.2.3.2

Multiply $6$ by $- 1$ .

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

Step 2.2.4

Reorder $2 i$ and $- 6$ .

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

Step 2.3

Simplify the denominator.

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Step 2.3.1

Add parentheses.

$\frac{- 6 + 2 i}{5 (i i)}$

Step 2.3.2

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

$\frac{- 6 + 2 i}{5 (i^{1} i)}$

Step 2.3.3

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

$\frac{- 6 + 2 i}{5 (i^{1} i^{1})}$

Step 2.3.4

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

$\frac{- 6 + 2 i}{5 i^{1 + 1}}$

Step 2.3.5

Add $1$ and $1$ .

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

Step 2.3.6

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

$\frac{- 6 + 2 i}{5 \cdot - 1}$

Step 3

Multiply $5$ by $- 1$ .

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

Step 4

Split the fraction $\frac{- 6 + 2 i}{- 5}$ into two fractions.

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

Step 5

Simplify each term.

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Step 5.1

Dividing two negative values results in a positive value.

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

Step 5.2

Move the negative in front of the fraction.

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