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Question Number 19758 by ajfour last updated on 15/Aug/17

Commented by ajfour last updated on 15/Aug/17

$$\mathrm{In}\mathrm{answer}\mathrm{to}\mathrm{Q}.19741$$

Answered by ajfour last updated on 15/Aug/17

$$\arg \left(\frac{\mathrm{z}-2}{\mathrm{z}+2}\right)=\frac{\pi }{6}\Rightarrow \theta -\varphi =\frac{\pi }{6}$$$$\mathrm{this}\mathrm{is}\mathrm{true}\mathrm{only}\mathrm{for}\mathrm{all}\mathrm{z}\mathrm{on}\mathrm{upper}$$$$\left(\mathrm{major}\right)\mathrm{arc}.\mathrm{If}\mathrm{z}\mathrm{be}\mathrm{on}\mathrm{lower}\mathrm{arc}$$$$\mathrm{then}\theta -\varphi =-\frac{5\pi }{6}=-(\pi -\frac{\pi }{6}).$$

Commented by Tinkutara last updated on 15/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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