Write in Standard Form 3/(2i-5)

$\frac{3}{2 i - 5}$

Multiply the numerator and denominator of $\frac{3}{- 5 + 2 i}$ by the conjugate of $- 5 + 2 i$ to make the denominator real.

$\frac{3}{- 5 + 2 i} \cdot \frac{- 5 - 2 i}{- 5 - 2 i}$

Multiply.

Combine.

$\frac{3 (- 5 - 2 i)}{(- 5 + 2 i) (- 5 - 2 i)}$

Simplify the numerator.

Apply the distributive property.

$\frac{3 \cdot - 5 + 3 (- 2 i)}{(- 5 + 2 i) (- 5 - 2 i)}$

Multiply $3$ by $- 5$ .

$\frac{- 15 + 3 (- 2 i)}{(- 5 + 2 i) (- 5 - 2 i)}$

Multiply $- 2$ by $3$ .

$\frac{- 15 - 6 i}{(- 5 + 2 i) (- 5 - 2 i)}$

Simplify the denominator.

Expand $(- 5 + 2 i) (- 5 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{- 15 - 6 i}{- 5 (- 5 - 2 i) + 2 i (- 5 - 2 i)}$

Apply the distributive property.

$\frac{- 15 - 6 i}{- 5 \cdot - 5 - 5 (- 2 i) + 2 i (- 5 - 2 i)}$

Apply the distributive property.

$\frac{- 15 - 6 i}{- 5 \cdot - 5 - 5 (- 2 i) + 2 i \cdot - 5 + 2 i (- 2 i)}$

Simplify.

Multiply $- 5$ by $- 5$ .

$\frac{- 15 - 6 i}{25 - 5 (- 2 i) + 2 i \cdot - 5 + 2 i (- 2 i)}$

Multiply $- 2$ by $- 5$ .

$\frac{- 15 - 6 i}{25 + 10 i + 2 i \cdot - 5 + 2 i (- 2 i)}$

Multiply $- 5$ by $2$ .

$\frac{- 15 - 6 i}{25 + 10 i - 10 i + 2 i (- 2 i)}$

Multiply $- 2$ by $2$ .

$\frac{- 15 - 6 i}{25 + 10 i - 10 i - 4 i i}$

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

$\frac{- 15 - 6 i}{25 + 10 i - 10 i - 4 (i^{1} i)}$

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

$\frac{- 15 - 6 i}{25 + 10 i - 10 i - 4 (i^{1} i^{1})}$

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

$\frac{- 15 - 6 i}{25 + 10 i - 10 i - 4 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 15 - 6 i}{25 + 10 i - 10 i - 4 i^{2}}$

Subtract $10 i$ from $10 i$ .

$\frac{- 15 - 6 i}{25 + 0 - 4 i^{2}}$

Add $25$ and $0$ .

$\frac{- 15 - 6 i}{25 - 4 i^{2}}$

Simplify each term.

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

$\frac{- 15 - 6 i}{25 - 4 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$\frac{- 15 - 6 i}{25 + 4}$

Add $25$ and $4$ .

$\frac{- 15 - 6 i}{29}$

Split the fraction $\frac{- 15 - 6 i}{29}$ into two fractions.

$\frac{- 15}{29} + \frac{- 6 i}{29}$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{15}{29} + \frac{- 6 i}{29}$

Move the negative in front of the fraction.

$- \frac{15}{29} - \frac{6 i}{29}$

Write in Standard Form 3/(2i-5)

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