simplify 5/(-3+4i)

Solution

simplify

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

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

Solution steps

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

Multiply by the conjugate

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

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

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

\frac{2 2}{2}

\frac{6}{7} + (- \frac{5}{14})

lo g_{2} (2 x + 2) \geq 1

1145 - 45

- 2 (1 + 2 n) < - 2 - 7 n