Algebra Examples

${(\frac{3 - 4 i}{5})}^{- 1}$

Step 1

Split the fraction $\frac{3 - 4 i}{5}$ into two fractions.

${(\frac{3}{5} + \frac{- 4 i}{5})}^{- 1}$

Step 2

Move the negative in front of the fraction.

${(\frac{3}{5} - \frac{4 i}{5})}^{- 1}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{\frac{3}{5} - \frac{4 i}{5}}$

Step 4

Combine the numerators over the common denominator.

$\frac{1}{\frac{3 - 4 i}{5}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{5}{3 - 4 i}$

Step 6

Multiply $\frac{5}{3 - 4 i}$ by $1$ .

$\frac{5}{3 - 4 i}$