Find the Complex Conjugate (3-2i)/(5i)

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

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

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

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $- 2 i i$ .

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

$\frac{3 i - 2 (i^{1} i)}{5 i i}$

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

$\frac{3 i - 2 (i^{1} i^{1})}{5 i i}$

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

$\frac{3 i - 2 i^{1 + 1}}{5 i i}$

Add $1$ and $1$ .

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

Simplify each term.

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

$\frac{3 i - 2 \cdot - 1}{5 i i}$

Multiply $- 2$ by $- 1$ .

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

Reorder $3 i$ and $2$ .

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

Simplify the denominator.

Add parentheses.

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

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

$\frac{2 + 3 i}{5 (i^{1} i)}$

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

$\frac{2 + 3 i}{5 (i^{1} i^{1})}$

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

$\frac{2 + 3 i}{5 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 + 3 i}{5 i^{2}}$

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

$\frac{2 + 3 i}{5 \cdot - 1}$

Multiply $5$ by $- 1$ .

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

Split the fraction $\frac{2 + 3 i}{- 5}$ into two fractions.

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

Simplify each term.

Move the negative in front of the fraction.

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

Move the negative in front of the fraction.

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

To find the complex conjugate, negate the term with $i$ .

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

Find the Complex Conjugate (3-2i)/(5i)

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