simplify (-2)/(1+i)

Solution

simplify

\frac{- 2}{1 + i}

- 1 + i

Solution steps

\frac{- 2}{1 + i}

Multiply by the conjugate

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

= \frac{- 2 ( 1 - i )}{( 1 + i ) ( 1 - i )}

Simplify

\frac{- 2 ( 1 - i )}{( 1 + i ) ( 1 - i )} : \frac{- 2 + 2 i}{2}

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

Apply the fraction rule:

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

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

Simplify

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

= - 1 + i

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