If ${(\frac{1 + i}{1 - i})}^{3} - {(\frac{1 - i}{1 + i})}^{3} = x + i y$ then $(x, y)$ is

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$(- 2, 0)$

$(0, 2)$

$(2, 0)$

$(0, - 2)$

answer is D.

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Detailed Solution

$\begin{array}{l} E = \frac{(1 + i)^{6} - (1 - i)^{6}}{{(1 - i^{2})}^{3}} = \frac{(2 i)^{3} - (- 2 i)^{3}}{2^{3}} \\ = - i - i = 0 - 2 i = (0, - 2) \end{array}$

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