Rewrite in Standard Form 6/(2+3i)

$\frac{6}{2 + 3 i}$

Multiply the numerator and denominator of $\frac{6}{2 + 3 i}$ by the conjugate of $2 + 3 i$ to make the denominator real.

$\frac{6}{2 + 3 i} \cdot \frac{2 - 3 i}{2 - 3 i}$

Multiply.

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Combine.

$\frac{6 (2 - 3 i)}{(2 + 3 i) (2 - 3 i)}$

Simplify the numerator.

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Apply the distributive property.

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

Multiply $6$ by $2$ .

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

Multiply $- 3$ by $6$ .

$\frac{12 - 18 i}{(2 + 3 i) (2 - 3 i)}$

Simplify the denominator.

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

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Apply the distributive property.

$\frac{12 - 18 i}{2 (2 - 3 i) + 3 i (2 - 3 i)}$

Apply the distributive property.

$\frac{12 - 18 i}{2 \cdot 2 + 2 (- 3 i) + 3 i (2 - 3 i)}$

Apply the distributive property.

$\frac{12 - 18 i}{2 \cdot 2 + 2 (- 3 i) + 3 i \cdot 2 + 3 i (- 3 i)}$

Simplify.

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Multiply $2$ by $2$ .

$\frac{12 - 18 i}{4 + 2 (- 3 i) + 3 i \cdot 2 + 3 i (- 3 i)}$

Multiply $- 3$ by $2$ .

$\frac{12 - 18 i}{4 - 6 i + 3 i \cdot 2 + 3 i (- 3 i)}$

Multiply $2$ by $3$ .

$\frac{12 - 18 i}{4 - 6 i + 6 i + 3 i (- 3 i)}$

Multiply $- 3$ by $3$ .

$\frac{12 - 18 i}{4 - 6 i + 6 i - 9 i i}$

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

$\frac{12 - 18 i}{4 - 6 i + 6 i - 9 (i^{1} i)}$

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

$\frac{12 - 18 i}{4 - 6 i + 6 i - 9 (i^{1} i^{1})}$

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

$\frac{12 - 18 i}{4 - 6 i + 6 i - 9 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{12 - 18 i}{4 - 6 i + 6 i - 9 i^{2}}$

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

$\frac{12 - 18 i}{4 + 0 - 9 i^{2}}$

Add $4$ and $0$ .

$\frac{12 - 18 i}{4 - 9 i^{2}}$

Simplify each term.

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

$\frac{12 - 18 i}{4 - 9 \cdot - 1}$

Multiply $- 9$ by $- 1$ .

$\frac{12 - 18 i}{4 + 9}$

Add $4$ and $9$ .

$\frac{12 - 18 i}{13}$

Split the fraction $\frac{12 - 18 i}{13}$ into two fractions.

$\frac{12}{13} + \frac{- 18 i}{13}$

Move the negative in front of the fraction.

$\frac{12}{13} - \frac{18 i}{13}$

Rewrite in Standard Form 6/(2+3i)

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