simplify 5/(4-3i)

Solution

simplify

\frac{5}{4 - 3 i}

\frac{4}{5} + \frac{3}{5} i

Solution steps

\frac{5}{4 - 3 i}

Multiply by the conjugate

\frac{4 + 3 i}{4 + 3 i}

= \frac{5 ( 4 + 3 i )}{( 4 - 3 i ) ( 4 + 3 i )}

Simplify

\frac{5 ( 4 + 3 i )}{( 4 - 3 i ) ( 4 + 3 i )} : \frac{20 + 15 i}{25}

= \frac{20 + 15 i}{25}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{20}{25} + \frac{15}{25} i

Simplify

\frac{20}{25} + \frac{15}{25} i : \frac{4}{5} + \frac{3}{5} i

= \frac{4}{5} + \frac{3}{5} i

2 (- 6)

\frac{4}{3} + \frac{2}{3}

\frac{1}{6} + \frac{1}{10}

x^{3} - 10 x^{2} + 31 x - 30

\frac{x ^{2} - 2 x - 15}{x + 3}