What is (-5-6i)/(8+7i) ?

The solution to (-5-6i)/(8+7i) is -82/113-13/113 i

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simplify (-5-6i)/(8+7i)

simplify

\frac{- 5 - 6 i}{8 + 7 i}

- \frac{82}{113} - \frac{13}{113} i

Solution steps

\frac{- 5 - 6 i}{8 + 7 i}

Multiply by the conjugate

\frac{8 - 7 i}{8 - 7 i}

= \frac{( - 5 - 6 i ) ( 8 - 7 i )}{( 8 + 7 i ) ( 8 - 7 i )}

Simplify

\frac{( - 5 - 6 i ) ( 8 - 7 i )}{( 8 + 7 i ) ( 8 - 7 i )} : \frac{- 82 - 13 i}{113}

= \frac{- 82 - 13 i}{113}

Apply the fraction rule:

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

= \frac{- 82}{113} + \frac{- 13}{113} i

Simplify

\frac{- 82}{113} + \frac{- 13}{113} i : - \frac{82}{113} - \frac{13}{113} i

= - \frac{82}{113} - \frac{13}{113} i

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