Divide 4/(5i)

$\frac{4}{5 i}$

Step 1

Multiply the numerator and denominator of $\frac{4}{5 i}$ by the conjugate of $5 i$ to make the denominator real.

$\frac{4}{5 i} \cdot \frac{i}{i}$

Step 2

Multiply.

Combine.

$\frac{4 i}{5 i i}$

Simplify the denominator.

Add parentheses.

$\frac{4 i}{5 (i i)}$

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

$\frac{4 i}{5 (i^{1} i)}$

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

$\frac{4 i}{5 (i^{1} i^{1})}$

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

$\frac{4 i}{5 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{4 i}{5 i^{2}}$

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

$\frac{4 i}{5 \cdot - 1}$

Step 3

Multiply $5$ by $- 1$ .

$\frac{4 i}{- 5}$

Step 4

Move the negative in front of the fraction.

$- \frac{4 i}{5}$