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

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

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

simplify

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

- \frac{8}{17} + \frac{2}{17} i

Solution steps

\frac{- 2}{4 + i}

Multiply by the conjugate

\frac{4 - i}{4 - i}

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

Simplify

\frac{- 2 ( 4 - i )}{( 4 + i ) ( 4 - i )} : \frac{- 8 + 2 i}{17}

= \frac{- 8 + 2 i}{17}

Rewrite in standard complex form:

- \frac{8}{17} + \frac{2}{17} i

= - \frac{8}{17} + \frac{2}{17} i

- 56 + 50

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