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Question Number 180285 by Mastermind last updated on 09/Nov/22

$$\mathrm{Express}\mathrm{this}\mathrm{f}\left(\mathrm{z}\right)=\frac{2\mathrm{z}+\mathrm{i}}{\mathrm{z}+\mathrm{i}}\mathrm{in}\mathrm{polar}\mathrm{form}$$$$\mathrm{where}\mathrm{z}={\mathrm{re}}^{\mathrm{i}\theta }\left(\mathrm{polar}\mathrm{form}\right)$$$$$$

Commented by Frix last updated on 09/Nov/22

$$\mathrm{do}\mathrm{some}\mathrm{work}\mathrm{too}$$$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{similar}\mathrm{to}\mathrm{the}\mathrm{last}\mathrm{one},\mathrm{we}\mathrm{need}\mathrm{the}$$$$\mathrm{Cartesian}\mathrm{form}\mathrm{to}\mathrm{get}\mathrm{there}:$$$$f\left(z\right)=\frac{2r^2+3r\sin \theta +1}{r^2+2r\sin \theta +1}-\mathrm{i}\frac{r\cos \theta }{r^2+2r\sin \theta +1}=$$$$=\sqrt{\frac{4r^2+4r\sin \theta +1}{r^2+2r\sin \theta +1}}{\mathrm{e}}^{-\mathrm{i}\arctan \frac{r\cos \theta }{2r^2+3r\sin \theta +1}}$$

Commented by Mastermind last updated on 10/Nov/22

$$\mathrm{ok}$$

Commented by Mastermind last updated on 10/Nov/22

$$\mathrm{The}\mathrm{thing}\mathrm{is}\mathrm{kind}\mathrm{of}\mathrm{complex}\mathrm{ooo}$$

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