What is (5-8i)/(-1-4i) ?

The solution to (5-8i)/(-1-4i) is 27/17+28/17 i

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simplify (5-8i)/(-1-4i)

simplify

\frac{5 - 8 i}{- 1 - 4 i}

\frac{27}{17} + \frac{28}{17} i

Solution steps

\frac{5 - 8 i}{- 1 - 4 i}

Multiply by the conjugate

\frac{- 1 + 4 i}{- 1 + 4 i}

= \frac{( 5 - 8 i ) ( - 1 + 4 i )}{( - 1 - 4 i ) ( - 1 + 4 i )}

Simplify

\frac{( 5 - 8 i ) ( - 1 + 4 i )}{( - 1 - 4 i ) ( - 1 + 4 i )} : \frac{27 + 28 i}{17}

= \frac{27 + 28 i}{17}

Rewrite in standard complex form:

\frac{27}{17} + \frac{28}{17} i

= \frac{27}{17} + \frac{28}{17} i

(\frac{1}{2})^{\frac{1}{5}}

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