What is (1-2i)^{-2} ?

The solution to (1-2i)^{-2} is -3/25+4/25 i

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

simplify

(1 - 2 i)^{- 2}

- \frac{3}{25} + \frac{4}{25} i

Solution steps

(1 - 2 i)^{- 2}

Apply exponent rule:

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

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

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

Expand

(1 - 2 i)^{2} : - 4 i - 3

= \frac{1}{- 4 i - 3}

Rewrite

- 4 i - 3

in standard complex form:

- 3 - 4 i

= \frac{1}{- 3 - 4 i}

Multiply by the conjugate

\frac{- 3 + 4 i}{- 3 + 4 i}

= \frac{1 \cdot ( - 3 + 4 i )}{( - 3 - 4 i ) ( - 3 + 4 i )}

Simplify

\frac{1 \cdot ( - 3 + 4 i )}{( - 3 - 4 i ) ( - 3 + 4 i )} : \frac{- 3 + 4 i}{25}

= \frac{- 3 + 4 i}{25}

Rewrite in standard complex form:

- \frac{3}{25} + \frac{4}{25} i

= - \frac{3}{25} + \frac{4}{25} i

\frac{sin ( x ) - 1}{cos ^{2} ( x )}

- 4 \cdot (- 7)

\frac{3}{x + 1} - \frac{1}{x + 2}

lo g_{3} ((3)^{5})

x (2 x - 7)