Basic Math Examples

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

Step 1

Multiply the numerator and denominator of

$\frac{1 + 6 i}{5 i}$ by the conjugate of

$5 i$ to make the denominator real.

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

Step 2

Multiply.

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Step 2.1

Combine.

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

Step 2.2

Simplify the numerator.

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Step 2.2.1

Apply the distributive property.

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

Step 2.2.2

Multiply

$i$ by

$1$ .

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

Step 2.2.3

Multiply

$6 i i$ .

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Step 2.2.3.1

Raise

$i$ to the power of

$1$ .

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

Step 2.2.3.2

Raise

$i$ to the power of

$1$ .

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

Step 2.2.3.3

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.2.3.4

Add

$1$ and

$1$ .

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

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

Step 2.2.4

Simplify each term.

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Step 2.2.4.1

Rewrite

$i^{2}$ as

$- 1$ .

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

Step 2.2.4.2

Multiply

$6$ by

$- 1$ .

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

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

Step 2.2.5

Reorder

$i$ and

$- 6$ .

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

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

Step 2.3

Simplify the denominator.

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Step 2.3.1

Add parentheses.

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

Step 2.3.2

Raise

$i$ to the power of

$1$ .

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

Step 2.3.3

Raise

$i$ to the power of

$1$ .

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

Step 2.3.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.3.5

Add

$1$ and

$1$ .

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

Step 2.3.6

Rewrite

$i^{2}$ as

$- 1$ .

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

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

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

Step 3

Multiply

$5$ by

$- 1$ .

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

Step 4

Split the fraction

$\frac{- 6 + i}{- 5}$ into two fractions.

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

Step 5

Simplify each term.

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Step 5.1

Dividing two negative values results in a positive value.

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

Step 5.2

Move the negative in front of the fraction.

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$