simplify (1+i)^{-1}

Solution

simplify

(1 + i)^{- 1}

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

Solution steps

(1 + i)^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

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

= \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}

Rewrite in standard complex form:

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

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

(1 + i) + (1 - i)

(1 + \frac{1}{x})^{2} - (1 - \frac{1}{x})^{2}

(7 x^{2} + 3 x + 4) - (2 x^{2} + 6 x - 5)

(x - 2) (x - 3)

0.5 (- 8)^{2}