Write in Standard Form 9/(3-2i)

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

Step 1

Multiply the numerator and denominator of $\frac{9}{3 - 2 i}$ by the conjugate of $3 - 2 i$ to make the denominator real.

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

Step 2

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $9$ by $3$ .

$\frac{27 + 9 (2 i)}{(3 - 2 i) (3 + 2 i)}$

Multiply $2$ by $9$ .

$\frac{27 + 18 i}{(3 - 2 i) (3 + 2 i)}$

Simplify the denominator.

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

Apply the distributive property.

$\frac{27 + 18 i}{3 (3 + 2 i) - 2 i (3 + 2 i)}$

Apply the distributive property.

$\frac{27 + 18 i}{3 \cdot 3 + 3 (2 i) - 2 i (3 + 2 i)}$

Apply the distributive property.

$\frac{27 + 18 i}{3 \cdot 3 + 3 (2 i) - 2 i \cdot 3 - 2 i (2 i)}$

Simplify.

Multiply $3$ by $3$ .

$\frac{27 + 18 i}{9 + 3 (2 i) - 2 i \cdot 3 - 2 i (2 i)}$

Multiply $2$ by $3$ .

$\frac{27 + 18 i}{9 + 6 i - 2 i \cdot 3 - 2 i (2 i)}$

Multiply $3$ by $- 2$ .

$\frac{27 + 18 i}{9 + 6 i - 6 i - 2 i (2 i)}$

Multiply $2$ by $- 2$ .

$\frac{27 + 18 i}{9 + 6 i - 6 i - 4 i i}$

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

$\frac{27 + 18 i}{9 + 6 i - 6 i - 4 (i^{1} i)}$

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

$\frac{27 + 18 i}{9 + 6 i - 6 i - 4 (i^{1} i^{1})}$

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

$\frac{27 + 18 i}{9 + 6 i - 6 i - 4 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{27 + 18 i}{9 + 6 i - 6 i - 4 i^{2}}$

Subtract $6 i$ from $6 i$ .

$\frac{27 + 18 i}{9 + 0 - 4 i^{2}}$

Add $9$ and $0$ .

$\frac{27 + 18 i}{9 - 4 i^{2}}$

Simplify each term.

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

$\frac{27 + 18 i}{9 - 4 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$\frac{27 + 18 i}{9 + 4}$

Add $9$ and $4$ .

$\frac{27 + 18 i}{13}$

Step 3

Split the fraction $\frac{27 + 18 i}{13}$ into two fractions.

$\frac{27}{13} + \frac{18 i}{13}$

Write in Standard Form 9/(3-2i)

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