simplify 1/(-1+i)

Solution

simplify

\frac{1}{- 1 + i}

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

Solution steps

\frac{1}{- 1 + i}

Multiply by the conjugate

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

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

Simplify

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

= \frac{- 1 - i}{2}

Apply the fraction rule:

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

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

Simplify

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

= - \frac{1}{2} - \frac{1}{2} i

\frac{a ^{10} b ^{20}}{a ^{2} b ^{10}}

4 x^{2} + 3 x - 27

3 x^{3} - x^{2} - 10 x

1 \frac{1}{2} \times \frac{1}{2}

\frac{2 a ^{2} + a - 3}{1 - a ^{3}}