What is (1-6i)/(8+7i) ?

The solution to (1-6i)/(8+7i) is -34/113-55/113 i

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simplify (1-6i)/(8+7i)

simplify

\frac{1 - 6 i}{8 + 7 i}

- \frac{34}{113} - \frac{55}{113} i

Solution steps

\frac{1 - 6 i}{8 + 7 i}

Multiply by the conjugate

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

= \frac{( 1 - 6 i ) ( 8 - 7 i )}{( 8 + 7 i ) ( 8 - 7 i )}

Simplify

\frac{( 1 - 6 i ) ( 8 - 7 i )}{( 8 + 7 i ) ( 8 - 7 i )} : \frac{- 34 - 55 i}{113}

= \frac{- 34 - 55 i}{113}

Apply the fraction rule:

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

= \frac{- 34}{113} + \frac{- 55}{113} i

Simplify

\frac{- 34}{113} + \frac{- 55}{113} i : - \frac{34}{113} - \frac{55}{113} i

= - \frac{34}{113} - \frac{55}{113} i

(x - 8) (x - 4)

- 4 y - 4 + (- 3)

8343

\frac{5 - 3}{5 + 3}