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

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

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

simplify

(2 - 2 i)^{- 1}

\frac{2 ( i + 1 ) ( 1 + i )}{4}

Solution steps

(2 - 2 i)^{- 1}

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

Apply exponent rule:

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

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

Rationalize

\frac{1}{2 - 2 i} : \frac{2 ( 1 + i ) ( i + 1 )}{4}

= \frac{2 ( i + 1 ) ( 1 + i )}{4}

\frac{x ^{2} + 5 x + 4}{x ^{2} + 3 x - 4}

10 x + 3 y + z - (5 x - 8 y + 3 z + 5 x - 2 y - 5 z)

(- 3) (4)

2 x^{2} + 4 x - 4

0.004

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