Algebra Examples

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

Step 1

Multiply the numerator and denominator of $\frac{4}{2 + 3 i}$ by the conjugate of $2 + 3 i$ to make the denominator real.

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

Step 2

Multiply.

Tap for more steps...

Step 2.1

Combine.

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

Step 2.2

Simplify the numerator.

Tap for more steps...

Step 2.2.1

Apply the distributive property.

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

Step 2.2.2

Multiply $4$ by $2$ .

$\frac{8 + 4 (- 3 i)}{(2 + 3 i) (2 - 3 i)}$

Step 2.2.3

Multiply $- 3$ by $4$ .

$\frac{8 - 12 i}{(2 + 3 i) (2 - 3 i)}$

Step 2.3

Simplify the denominator.

Tap for more steps...

Step 2.3.1

Expand $(2 + 3 i) (2 - 3 i)$ using the FOIL Method.

Tap for more steps...

Step 2.3.1.1

Apply the distributive property.

$\frac{8 - 12 i}{2 (2 - 3 i) + 3 i (2 - 3 i)}$

Step 2.3.1.2

Apply the distributive property.

$\frac{8 - 12 i}{2 \cdot 2 + 2 (- 3 i) + 3 i (2 - 3 i)}$

Step 2.3.1.3

Apply the distributive property.

$\frac{8 - 12 i}{2 \cdot 2 + 2 (- 3 i) + 3 i \cdot 2 + 3 i (- 3 i)}$

Step 2.3.2

Simplify.

Tap for more steps...

Step 2.3.2.1

Multiply $2$ by $2$ .

$\frac{8 - 12 i}{4 + 2 (- 3 i) + 3 i \cdot 2 + 3 i (- 3 i)}$

Step 2.3.2.2

Multiply $- 3$ by $2$ .

$\frac{8 - 12 i}{4 - 6 i + 3 i \cdot 2 + 3 i (- 3 i)}$

Step 2.3.2.3

Multiply $2$ by $3$ .

$\frac{8 - 12 i}{4 - 6 i + 6 i + 3 i (- 3 i)}$

Step 2.3.2.4

Multiply $- 3$ by $3$ .

$\frac{8 - 12 i}{4 - 6 i + 6 i - 9 i i}$

Step 2.3.2.5

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

$\frac{8 - 12 i}{4 - 6 i + 6 i - 9 (i^{1} i)}$

Step 2.3.2.6

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

$\frac{8 - 12 i}{4 - 6 i + 6 i - 9 (i^{1} i^{1})}$

Step 2.3.2.7

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

$\frac{8 - 12 i}{4 - 6 i + 6 i - 9 i^{1 + 1}}$

Step 2.3.2.8

Add $1$ and $1$ .

$\frac{8 - 12 i}{4 - 6 i + 6 i - 9 i^{2}}$

Step 2.3.2.9

Add $- 6 i$ and $6 i$ .

$\frac{8 - 12 i}{4 + 0 - 9 i^{2}}$

Step 2.3.2.10

Add $4$ and $0$ .

$\frac{8 - 12 i}{4 - 9 i^{2}}$

Step 2.3.3

Simplify each term.

Tap for more steps...

Step 2.3.3.1

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

$\frac{8 - 12 i}{4 - 9 \cdot - 1}$

Step 2.3.3.2

Multiply $- 9$ by $- 1$ .

$\frac{8 - 12 i}{4 + 9}$

Step 2.3.4

Add $4$ and $9$ .

$\frac{8 - 12 i}{13}$

Step 3

Split the fraction $\frac{8 - 12 i}{13}$ into two fractions.

$\frac{8}{13} + \frac{- 12 i}{13}$

Step 4

Move the negative in front of the fraction.

$\frac{8}{13} - \frac{12 i}{13}$

Enter YOUR Problem