Basic Math Examples

$\frac{4 - 6 i}{9 i}$

Step 1

Multiply the numerator and denominator of $\frac{4 - 6 i}{9 i}$ by the conjugate of $9 i$ to make the denominator real.

$\frac{4 - 6 i}{9 i} \cdot \frac{i}{i}$

Step 2

Multiply.

Tap for more steps...

Step 2.1

Combine.

$\frac{(4 - 6 i) i}{9 i i}$

Step 2.2

Simplify the numerator.

Tap for more steps...

Step 2.2.1

Apply the distributive property.

$\frac{4 i - 6 i i}{9 i i}$

Step 2.2.2

Multiply $- 6 i i$ .

Tap for more steps...

Step 2.2.2.1

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

$\frac{4 i - 6 (i^{1} i)}{9 i i}$

Step 2.2.2.2

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

$\frac{4 i - 6 (i^{1} i^{1})}{9 i i}$

Step 2.2.2.3

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

$\frac{4 i - 6 i^{1 + 1}}{9 i i}$

Step 2.2.2.4

Add $1$ and $1$ .

$\frac{4 i - 6 i^{2}}{9 i i}$

Step 2.2.3

Simplify each term.

Tap for more steps...

Step 2.2.3.1

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

$\frac{4 i - 6 \cdot - 1}{9 i i}$

Step 2.2.3.2

Multiply $- 6$ by $- 1$ .

$\frac{4 i + 6}{9 i i}$

Step 2.2.4

Reorder $4 i$ and $6$ .

$\frac{6 + 4 i}{9 i i}$

Step 2.3

Simplify the denominator.

Tap for more steps...

Step 2.3.1

Add parentheses.

$\frac{6 + 4 i}{9 (i i)}$

Step 2.3.2

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

$\frac{6 + 4 i}{9 (i^{1} i)}$

Step 2.3.3

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

$\frac{6 + 4 i}{9 (i^{1} i^{1})}$

Step 2.3.4

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

$\frac{6 + 4 i}{9 i^{1 + 1}}$

Step 2.3.5

Add $1$ and $1$ .

$\frac{6 + 4 i}{9 i^{2}}$

Step 2.3.6

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

$\frac{6 + 4 i}{9 \cdot - 1}$

Step 3

Multiply $9$ by $- 1$ .

$\frac{6 + 4 i}{- 9}$

Step 4

Split the fraction $\frac{6 + 4 i}{- 9}$ into two fractions.

$\frac{6}{- 9} + \frac{4 i}{- 9}$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Cancel the common factor of $6$ and $- 9$ .

Tap for more steps...

Step 5.1.1

Factor $3$ out of $6$ .

$\frac{3 (2)}{- 9} + \frac{4 i}{- 9}$

Step 5.1.2

Cancel the common factors.

Tap for more steps...

Step 5.1.2.1

Factor $3$ out of $- 9$ .

$\frac{3 \cdot 2}{3 \cdot - 3} + \frac{4 i}{- 9}$

Step 5.1.2.2

Cancel the common factor.

$\frac{3 \cdot 2}{3 \cdot - 3} + \frac{4 i}{- 9}$

Step 5.1.2.3

Rewrite the expression.

$\frac{2}{- 3} + \frac{4 i}{- 9}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{2}{3} + \frac{4 i}{- 9}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{2}{3} - \frac{4 i}{9}$