What is (-19-22i)/(1+8i) ?

The solution to (-19-22i)/(1+8i) is -3+2i

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simplify (-19-22i)/(1+8i)

simplify

\frac{- 19 - 22 i}{1 + 8 i}

- 3 + 2 i

Solution steps

\frac{- 19 - 22 i}{1 + 8 i}

Multiply by the conjugate

\frac{1 - 8 i}{1 - 8 i}

= \frac{( - 19 - 22 i ) ( 1 - 8 i )}{( 1 + 8 i ) ( 1 - 8 i )}

Simplify

\frac{( - 19 - 22 i ) ( 1 - 8 i )}{( 1 + 8 i ) ( 1 - 8 i )} : \frac{- 195 + 130 i}{65}

= \frac{- 195 + 130 i}{65}

Apply the fraction rule:

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

= \frac{- 195}{65} + \frac{130}{65} i

Simplify

\frac{- 195}{65} + \frac{130}{65} i : - 3 + 2 i

= - 3 + 2 i

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