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Popular >

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

Solution

simplify

(1 - 2 i)^{- 1}

Solution

\frac{1}{5} + \frac{2}{5} i

Solution steps

(1 - 2 i)^{- 1}

Apply exponent rule:

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

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

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

Multiply by the conjugate

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

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

Simplify

\frac{1 \cdot ( 1 + 2 i )}{( 1 - 2 i ) ( 1 + 2 i )} : \frac{1 + 2 i}{5}

= \frac{1 + 2 i}{5}

Rewrite in standard complex form:

\frac{1}{5} + \frac{2}{5} i

= \frac{1}{5} + \frac{2}{5} i

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Frequently Asked Questions (FAQ)

What is (1-2i)^{-1} ?
The solution to (1-2i)^{-1} is 1/5+2/5 i