What is (-13-i)/(3-5i) ?

The solution to (-13-i)/(3-5i) is -1-2i

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simplify (-13-i)/(3-5i)

simplify

\frac{- 13 - i}{3 - 5 i}

- 1 - 2 i

Solution steps

\frac{- 13 - i}{3 - 5 i}

Multiply by the conjugate

\frac{3 + 5 i}{3 + 5 i}

= \frac{( - 13 - i ) ( 3 + 5 i )}{( 3 - 5 i ) ( 3 + 5 i )}

Simplify

\frac{( - 13 - i ) ( 3 + 5 i )}{( 3 - 5 i ) ( 3 + 5 i )} : \frac{- 34 - 68 i}{34}

= \frac{- 34 - 68 i}{34}

Apply the fraction rule:

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

= \frac{- 34}{34} + \frac{- 68}{34} i

Simplify

\frac{- 34}{34} + \frac{- 68}{34} i : - 1 - 2 i

= - 1 - 2 i

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