Divide -2/(5i)

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

Step 1

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

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

Step 2

Multiply.

Combine.

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

Simplify the denominator.

Add parentheses.

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Step 3

Multiply $5$ by $- 1$ .

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

Step 4

Move the negative in front of the fraction.

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

Step 5

Multiply $- - \frac{2 i}{5}$ .

Multiply $- 1$ by $- 1$ .

$1 \frac{2 i}{5}$

Multiply $\frac{2 i}{5}$ by $1$ .

$\frac{2 i}{5}$