Precalculus Examples

$\frac{\frac{1}{7} + i}{\frac{5}{i}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{1}{7} + i) \frac{i}{5}$

Step 2

Apply the distributive property.

$\frac{1}{7} \cdot \frac{i}{5} + i \frac{i}{5}$

Step 3

Multiply $\frac{1}{7} \cdot \frac{i}{5}$ .

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Step 3.1

Multiply $\frac{1}{7}$ by $\frac{i}{5}$ .

$\frac{i}{7 \cdot 5} + i \frac{i}{5}$

Step 3.2

Multiply $7$ by $5$ .

$\frac{i}{35} + i \frac{i}{5}$

Step 4

Multiply $i \frac{i}{5}$ .

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Step 4.1

Combine $i$ and $\frac{i}{5}$ .

$\frac{i}{35} + \frac{i i}{5}$

Step 4.2

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

$\frac{i}{35} + \frac{i^{1} i}{5}$

Step 4.3

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

$\frac{i}{35} + \frac{i^{1} i^{1}}{5}$

Step 4.4

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

$\frac{i}{35} + \frac{i^{1 + 1}}{5}$

Step 4.5

Add $1$ and $1$ .

$\frac{i}{35} + \frac{i^{2}}{5}$

Step 5

Simplify each term.

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Step 5.1

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

$\frac{i}{35} + \frac{- 1}{5}$

Step 5.2

Move the negative in front of the fraction.

$\frac{i}{35} - \frac{1}{5}$

Step 6

Reorder $\frac{i}{35}$ and $- \frac{1}{5}$ .

$- \frac{1}{5} + \frac{i}{35}$