Finite Math Examples

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

Step 1

Multiply the numerator and denominator of $\frac{- 1 - 5 i}{7 i}$ by the conjugate of $7 i$ to make the denominator real.

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

Step 2

Multiply.

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Step 2.1

Combine.

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

Step 2.2

Simplify the numerator.

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Step 2.2.1

Apply the distributive property.

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

Step 2.2.2

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

$\frac{- i - 5 i i}{7 i i}$

Step 2.2.3

Multiply $- 5 i i$ .

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Step 2.2.3.1

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

$\frac{- i - 5 (i^{1} i)}{7 i i}$

Step 2.2.3.2

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

$\frac{- i - 5 (i^{1} i^{1})}{7 i i}$

Step 2.2.3.3

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

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

Step 2.2.3.4

Add $1$ and $1$ .

$\frac{- i - 5 i^{2}}{7 i i}$

Step 2.2.4

Simplify each term.

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Step 2.2.4.1

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

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

Step 2.2.4.2

Multiply $- 5$ by $- 1$ .

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

Step 2.2.5

Reorder $- i$ and $5$ .

$\frac{5 - i}{7 i i}$

Step 2.3

Simplify the denominator.

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Step 2.3.1

Add parentheses.

$\frac{5 - i}{7 (i i)}$

Step 2.3.2

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

$\frac{5 - i}{7 (i^{1} i)}$

Step 2.3.3

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

$\frac{5 - i}{7 (i^{1} i^{1})}$

Step 2.3.4

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

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

Step 2.3.5

Add $1$ and $1$ .

$\frac{5 - i}{7 i^{2}}$

Step 2.3.6

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

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

Step 3

Multiply $7$ by $- 1$ .

$\frac{5 - i}{- 7}$

Step 4

Split the fraction $\frac{5 - i}{- 7}$ into two fractions.

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

Step 5

Simplify each term.

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Step 5.1

Move the negative in front of the fraction.

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

Step 5.2

Dividing two negative values results in a positive value.

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