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Question

(C) Let $z = x + iy$. Given $0 < 	ext{amp}(z) < \pi$,the complex number $z$ lies in the upper half-plane.Since $	ext{amp}(z) = 	heta$,we have $	ex

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$\pi$

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(C) Let $z = x + iy$. Given $0 Since $	ext{amp}(z) = 	heta$,we have $	ext{amp}(-z) = 	ext{amp}(-(x + iy)) = 	ext{amp}(-x - iy)$.Since $z$ is in the first or second quadrant,$-z$ is in the third or fourth quadrant.Specifically,if $	ext{amp}(z) = 	heta$,then $	ext{amp}(-z) = 	heta - \pi$ (if $	heta > 0$) or $	heta + \pi$ (if $	heta Given $0 Therefore,$	ext{amp}(z) - 	ext{amp}(-z) = 	ext{amp}(z) - (	ext{amp}(z) - \pi) = \pi$.

If $0 < \text{amp}(z) < \pi$,then $\text{amp}(z) - \text{amp}(-z) = $

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