simplify 9/(-1+5i)

Solution

simplify

\frac{9}{- 1 + 5 i}

- \frac{9}{26} - \frac{45}{26} i

Solution steps

\frac{9}{- 1 + 5 i}

Multiply by the conjugate

\frac{- 1 - 5 i}{- 1 - 5 i}

= \frac{9 ( - 1 - 5 i )}{( - 1 + 5 i ) ( - 1 - 5 i )}

Simplify

\frac{9 ( - 1 - 5 i )}{( - 1 + 5 i ) ( - 1 - 5 i )} : \frac{- 9 - 45 i}{26}

= \frac{- 9 - 45 i}{26}

Apply the fraction rule:

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

= \frac{- 9}{26} + \frac{- 45}{26} i

Simplify

\frac{- 9}{26} + \frac{- 45}{26} i : - \frac{9}{26} - \frac{45}{26} i

= - \frac{9}{26} - \frac{45}{26} i

(\frac{3}{2})^{2}

2 x^{2} - 5 x + 7 = 0

(\frac{2 a ^{- 1} b}{a ^{2} b ^{- 3}})^{- 3}

r^{2} + 64 r = 0

n^{2} = - 72