What is (7-6i)/(6+9i) ?

The solution to (7-6i)/(6+9i) is -4/39-11/13 i

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simplify (7-6i)/(6+9i)

simplify

\frac{7 - 6 i}{6 + 9 i}

- \frac{4}{39} - \frac{11}{13} i

Solution steps

\frac{7 - 6 i}{6 + 9 i}

Multiply by the conjugate

\frac{6 - 9 i}{6 - 9 i}

= \frac{( 7 - 6 i ) ( 6 - 9 i )}{( 6 + 9 i ) ( 6 - 9 i )}

Simplify

\frac{( 7 - 6 i ) ( 6 - 9 i )}{( 6 + 9 i ) ( 6 - 9 i )} : \frac{- 12 - 99 i}{117}

= \frac{- 12 - 99 i}{117}

Apply the fraction rule:

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

= \frac{- 12}{117} + \frac{- 99}{117} i

Simplify

\frac{- 12}{117} + \frac{- 99}{117} i : - \frac{4}{39} - \frac{11}{13} i

= - \frac{4}{39} - \frac{11}{13} i

(- \frac{4}{9}) + (- \frac{6}{18})

5 x + 5 x

20 \cdot \frac{1}{3}

\frac{2}{7 - 11}

2 x^{- 5}