What is (7-2i)/(2+9i) ?

The solution to (7-2i)/(2+9i) is -4/85-67/85 i

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simplify (7-2i)/(2+9i)

simplify

\frac{7 - 2 i}{2 + 9 i}

- \frac{4}{85} - \frac{67}{85} i

Solution steps

\frac{7 - 2 i}{2 + 9 i}

Multiply by the conjugate

\frac{2 - 9 i}{2 - 9 i}

= \frac{( 7 - 2 i ) ( 2 - 9 i )}{( 2 + 9 i ) ( 2 - 9 i )}

Simplify

\frac{( 7 - 2 i ) ( 2 - 9 i )}{( 2 + 9 i ) ( 2 - 9 i )} : \frac{- 4 - 67 i}{85}

= \frac{- 4 - 67 i}{85}

Apply the fraction rule:

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

= \frac{- 4}{85} + \frac{- 67}{85} i

Simplify

\frac{- 4}{85} + \frac{- 67}{85} i : - \frac{4}{85} - \frac{67}{85} i

= - \frac{4}{85} - \frac{67}{85} i

(2 x - 5) (x^{2} - x + 1)

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