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Popular >

simplify (2+2i)^{-1}

Solution

simplify

(2 + 2 i)^{- 1}

Solution

\frac{1}{4} - \frac{1}{4} i

Solution steps

(2 + 2 i)^{- 1}

Apply exponent rule:

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

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

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

Multiply by the conjugate

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

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

Simplify

\frac{1 \cdot ( 2 - 2 i )}{( 2 + 2 i ) ( 2 - 2 i )} : \frac{2 - 2 i}{8}

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

Apply the fraction rule:

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

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

Simplify

\frac{2}{8} + \frac{- 2}{8} i : \frac{1}{4} - \frac{1}{4} i

= \frac{1}{4} - \frac{1}{4} i

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Frequently Asked Questions (FAQ)

What is (2+2i)^{-1} ?
The solution to (2+2i)^{-1} is 1/4-1/4 i