What is (4+4i)/(-2-8i) ?

The solution to (4+4i)/(-2-8i) is -10/17+6/17 i

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simplify (4+4i)/(-2-8i)

simplify

\frac{4 + 4 i}{- 2 - 8 i}

- \frac{10}{17} + \frac{6}{17} i

Solution steps

\frac{4 + 4 i}{- 2 - 8 i}

Multiply by the conjugate

\frac{- 2 + 8 i}{- 2 + 8 i}

= \frac{( 4 + 4 i ) ( - 2 + 8 i )}{( - 2 - 8 i ) ( - 2 + 8 i )}

Simplify

\frac{( 4 + 4 i ) ( - 2 + 8 i )}{( - 2 - 8 i ) ( - 2 + 8 i )} : \frac{- 40 + 24 i}{68}

= \frac{- 40 + 24 i}{68}

Apply the fraction rule:

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

= \frac{- 40}{68} + \frac{24}{68} i

Simplify

\frac{- 40}{68} + \frac{24}{68} i : - \frac{10}{17} + \frac{6}{17} i

= - \frac{10}{17} + \frac{6}{17} i

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