simplify 5/(-5+4i)

Solution

simplify

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

- \frac{25}{41} - \frac{20}{41} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{5 ( - 5 - 4 i )}{( - 5 + 4 i ) ( - 5 - 4 i )} : \frac{- 25 - 20 i}{41}

= \frac{- 25 - 20 i}{41}

Apply the fraction rule:

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

= \frac{- 25}{41} + \frac{- 20}{41} i

Simplify

\frac{- 25}{41} + \frac{- 20}{41} i : - \frac{25}{41} - \frac{20}{41} i

= - \frac{25}{41} - \frac{20}{41} i

- 6 (2 x + 1) - 3 (x - 4) = - 15 x + 1

16 \leq \frac{n}{- 2} + 8

2 x - 6 \geq 4 and - 5 x - 7 \geq 8

\frac{2 x - 3}{4} - 3 x = \frac{7}{4} - \frac{x + 1}{3}

(a^{9})^{\frac{1}{3}}