Question

Find the argument of the following complex number:
$({ - 1 + ( \sqrt{2} - 1 )i})^{2}$

Answer 1

Solution:-

given by:-

$({ - 1 + ( \sqrt{2} - 1 )i})^{2} \\ 1 + ( { \sqrt{2} - 1) }^{2} \times ( - 1) - 2 i\sqrt{2} + i \\ 1 - 2 - 1 + 2 \sqrt{2} - 2i \sqrt{2} + i \\ - 2(1 - \sqrt{2} + i \sqrt{2} - \frac{i}{2} )$