Divide 13/(2-3i)

$\frac{13}{2 - 3 i}$

Multiply the numerator and denominator of $\frac{13}{2 - 3 i}$ by the conjugate of $2 - 3 i$ to make the denominator real.

$\frac{13}{2 - 3 i} \cdot \frac{2 + 3 i}{2 + 3 i}$

Multiply.

Combine.

$\frac{13 (2 + 3 i)}{(2 - 3 i) (2 + 3 i)}$

Simplify the numerator.

Apply the distributive property.

$\frac{13 \cdot 2 + 13 (3 i)}{(2 - 3 i) (2 + 3 i)}$

Multiply $13$ by $2$ .

$\frac{26 + 13 (3 i)}{(2 - 3 i) (2 + 3 i)}$

Multiply $3$ by $13$ .

$\frac{26 + 39 i}{(2 - 3 i) (2 + 3 i)}$

Simplify the denominator.

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

Apply the distributive property.

$\frac{26 + 39 i}{2 (2 + 3 i) - 3 i (2 + 3 i)}$

Apply the distributive property.

$\frac{26 + 39 i}{2 \cdot 2 + 2 (3 i) - 3 i (2 + 3 i)}$

Apply the distributive property.

$\frac{26 + 39 i}{2 \cdot 2 + 2 (3 i) - 3 i \cdot 2 - 3 i (3 i)}$

Simplify.

Multiply $2$ by $2$ .

$\frac{26 + 39 i}{4 + 2 (3 i) - 3 i \cdot 2 - 3 i (3 i)}$

Multiply $3$ by $2$ .

$\frac{26 + 39 i}{4 + 6 i - 3 i \cdot 2 - 3 i (3 i)}$

Multiply $2$ by $- 3$ .

$\frac{26 + 39 i}{4 + 6 i - 6 i - 3 i (3 i)}$

Multiply $3$ by $- 3$ .

$\frac{26 + 39 i}{4 + 6 i - 6 i - 9 i i}$

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

$\frac{26 + 39 i}{4 + 6 i - 6 i - 9 (i^{1} i)}$

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

$\frac{26 + 39 i}{4 + 6 i - 6 i - 9 (i^{1} i^{1})}$

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

$\frac{26 + 39 i}{4 + 6 i - 6 i - 9 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{26 + 39 i}{4 + 6 i - 6 i - 9 i^{2}}$

Subtract $6 i$ from $6 i$ .

$\frac{26 + 39 i}{4 + 0 - 9 i^{2}}$

Add $4$ and $0$ .

$\frac{26 + 39 i}{4 - 9 i^{2}}$

Simplify each term.

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

$\frac{26 + 39 i}{4 - 9 \cdot - 1}$

Multiply $- 9$ by $- 1$ .

$\frac{26 + 39 i}{4 + 9}$

Add $4$ and $9$ .

$\frac{26 + 39 i}{13}$

Cancel the common factor of $26 + 39 i$ and $13$ .

Factor $13$ out of $26$ .

$\frac{13 \cdot 2 + 39 i}{13}$

Factor $13$ out of $39 i$ .

$\frac{13 \cdot 2 + 13 (3 i)}{13}$

Factor $13$ out of $13 (2) + 13 (3 i)$ .

$\frac{13 (2 + 3 i)}{13}$

Cancel the common factors.

Factor $13$ out of $13$ .

$\frac{13 (2 + 3 i)}{13 (1)}$

Cancel the common factor.

$\frac{13 (2 + 3 i)}{13 \cdot 1}$

Rewrite the expression.

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

Divide $2 + 3 i$ by $1$ .

$2 + 3 i$

Divide 13/(2-3i)

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