What is (9-i)/(-4+5i) ?

The solution to (9-i)/(-4+5i) is -1-i

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simplify (9-i)/(-4+5i)

simplify

\frac{9 - i}{- 4 + 5 i}

- 1 - i

Solution steps

\frac{9 - i}{- 4 + 5 i}

Multiply by the conjugate

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

= \frac{( 9 - i ) ( - 4 - 5 i )}{( - 4 + 5 i ) ( - 4 - 5 i )}

Simplify

\frac{( 9 - i ) ( - 4 - 5 i )}{( - 4 + 5 i ) ( - 4 - 5 i )} : \frac{- 41 - 41 i}{41}

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

Apply the fraction rule:

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

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

Simplify

\frac{- 41}{41} + \frac{- 41}{41} i : - 1 - i

= - 1 - i

\frac{( x ^{2} + y ^{2} )}{x ^{2} - y ^{2}} + \frac{y}{x + y} - \frac{x}{x - y}

\frac{n ^{2} + 2 n - 24}{n ^{2} - 11 n + 28}

- 9 x^{2} - 6 x - 1 = 0

\frac{4}{3} \cdot π

\frac{1}{5} x + \frac{1}{3} = \frac{4}{3}