find-arg-z-given-that-z-1-i-1-i-

Question Number 84564 by Rio Michael last updated on 14/Mar/20

find \arg (z) given that z = \frac{1 + i}{1 - i}

Commented by mr W last updated on 14/Mar/20

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

= \cos (\frac{π}{2}) + i \sin (\frac{π}{2})

\Rightarrow a r g (z) = \frac{π}{2}

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