simplify 9/(-10-5i)

Solution

simplify

\frac{9}{- 10 - 5 i}

- \frac{18}{25} + \frac{9}{25} i

Solution steps

\frac{9}{- 10 - 5 i}

Multiply by the conjugate

\frac{- 10 + 5 i}{- 10 + 5 i}

= \frac{9 ( - 10 + 5 i )}{( - 10 - 5 i ) ( - 10 + 5 i )}

Simplify

\frac{9 ( - 10 + 5 i )}{( - 10 - 5 i ) ( - 10 + 5 i )} : \frac{- 90 + 45 i}{125}

= \frac{- 90 + 45 i}{125}

Apply the fraction rule:

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

= \frac{- 90}{125} + \frac{45}{125} i

Simplify

\frac{- 90}{125} + \frac{45}{125} i : - \frac{18}{25} + \frac{9}{25} i

= - \frac{18}{25} + \frac{9}{25} i

\frac{9}{3} - \frac{6}{10}

x^{4} - 4 x^{3} - x^{2} + 4 x = 0

1 + 3 p > 10

11 x^{3} y^{3} + 55 x^{5} y