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Popular >

simplify (1+i)^{-2}

Solution

simplify

(1 + i)^{- 2}

Solution

- \frac{1}{2} i

Solution steps

(1 + i)^{- 2}

Apply exponent rule:

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

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

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

Expand

(1 + i)^{2} : 2 i

= \frac{1}{2 i}

Multiply by the conjugate

\frac{- i}{- i}

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

Simplify

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

= \frac{- i}{2}

Rewrite in standard complex form:

- \frac{1}{2} i

= - \frac{1}{2} i

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Frequently Asked Questions (FAQ)

What is (1+i)^{-2} ?
The solution to (1+i)^{-2} is -1/2 i