Basic Math Examples

\frac{4 - 2 i}{3 i}

$\frac{4 - 2 i}{3 i}$

Step 1

Multiply the numerator and denominator of

\frac{4 - 2 i}{3 i}

$\frac{4 - 2 i}{3 i}$ by the conjugate of

3 i

$3 i$ to make the denominator real.

\frac{4 - 2 i}{3 i} \cdot \frac{i}{i}

$\frac{4 - 2 i}{3 i} \cdot \frac{i}{i}$

Step 2

Multiply.

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Step 2.1

Combine.

\frac{(4 - 2 i) i}{3 i i}

$\frac{(4 - 2 i) i}{3 i i}$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Apply the distributive property.

\frac{4 i - 2 i i}{3 i i}

$\frac{4 i - 2 i i}{3 i i}$

Step 2.2.2

Multiply

- 2 i i

$- 2 i i$ .

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Step 2.2.2.1

Raise

i

$i$ to the power of

1

$1$ .

\frac{4 i - 2 (i^{1} i)}{3 i i}

$\frac{4 i - 2 (i^{1} i)}{3 i i}$

Step 2.2.2.2

Raise

i

$i$ to the power of

1

$1$ .

\frac{4 i - 2 (i^{1} i^{1})}{3 i i}

$\frac{4 i - 2 (i^{1} i^{1})}{3 i i}$

Step 2.2.2.3

Use the power rule

a^{m} a^{n} = a^{m + n}

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

\frac{4 i - 2 i^{1 + 1}}{3 i i}

$\frac{4 i - 2 i^{1 + 1}}{3 i i}$

Step 2.2.2.4

Add

1

$1$ and

1

$1$ .

\frac{4 i - 2 i^{2}}{3 i i}

$\frac{4 i - 2 i^{2}}{3 i i}$

\frac{4 i - 2 i^{2}}{3 i i}

$\frac{4 i - 2 i^{2}}{3 i i}$

Step 2.2.3

Simplify each term.

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Step 2.2.3.1

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

\frac{4 i - 2 \cdot - 1}{3 i i}

$\frac{4 i - 2 \cdot - 1}{3 i i}$

Step 2.2.3.2

Multiply

- 2

$- 2$ by

- 1

$- 1$ .

\frac{4 i + 2}{3 i i}

$\frac{4 i + 2}{3 i i}$

\frac{4 i + 2}{3 i i}

$\frac{4 i + 2}{3 i i}$

Step 2.2.4

Reorder

4 i

$4 i$ and

2

$2$ .

\frac{2 + 4 i}{3 i i}

$\frac{2 + 4 i}{3 i i}$

\frac{2 + 4 i}{3 i i}

$\frac{2 + 4 i}{3 i i}$

Step 2.3

Simplify the denominator.

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Step 2.3.1

Add parentheses.

\frac{2 + 4 i}{3 (i i)}

$\frac{2 + 4 i}{3 (i i)}$

Step 2.3.2

Raise

i

$i$ to the power of

1

$1$ .

\frac{2 + 4 i}{3 (i^{1} i)}

$\frac{2 + 4 i}{3 (i^{1} i)}$

Step 2.3.3

Raise

i

$i$ to the power of

1

$1$ .

\frac{2 + 4 i}{3 (i^{1} i^{1})}

$\frac{2 + 4 i}{3 (i^{1} i^{1})}$

Step 2.3.4

Use the power rule

a^{m} a^{n} = a^{m + n}

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

\frac{2 + 4 i}{3 i^{1 + 1}}

$\frac{2 + 4 i}{3 i^{1 + 1}}$

Step 2.3.5

Add

1

$1$ and

1

$1$ .

\frac{2 + 4 i}{3 i^{2}}

$\frac{2 + 4 i}{3 i^{2}}$

Step 2.3.6

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

\frac{2 + 4 i}{3 \cdot - 1}

$\frac{2 + 4 i}{3 \cdot - 1}$

\frac{2 + 4 i}{3 \cdot - 1}

$\frac{2 + 4 i}{3 \cdot - 1}$

\frac{2 + 4 i}{3 \cdot - 1}

$\frac{2 + 4 i}{3 \cdot - 1}$

Step 3

Multiply

3

$3$ by

- 1

$- 1$ .

\frac{2 + 4 i}{- 3}

$\frac{2 + 4 i}{- 3}$

Step 4

Split the fraction

\frac{2 + 4 i}{- 3}

$\frac{2 + 4 i}{- 3}$ into two fractions.

\frac{2}{- 3} + \frac{4 i}{- 3}

$\frac{2}{- 3} + \frac{4 i}{- 3}$

Step 5

Simplify each term.

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Step 5.1

Move the negative in front of the fraction.

- \frac{2}{3} + \frac{4 i}{- 3}

$- \frac{2}{3} + \frac{4 i}{- 3}$

Step 5.2

Move the negative in front of the fraction.

- \frac{2}{3} - \frac{4 i}{3}

$- \frac{2}{3} - \frac{4 i}{3}$

- \frac{2}{3} - \frac{4 i}{3}

$- \frac{2}{3} - \frac{4 i}{3}$

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

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