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Question Number 192241 by yaslm last updated on 12/May/23

Answered by Frix last updated on 12/May/23

$$Z_1=\frac{\frac{1}{2}{\mathrm{e}}^{-\mathrm{i}x}}{1-\frac{1}{2}{\mathrm{e}}^{-\mathrm{i}x}}=-\frac{1-2\cos x}{5-4\cos x}-\frac{2\sin x}{5-4\cos x}\mathrm{i}$$$$Z_2=\frac{1}{1-\frac{1}{2}{\mathrm{e}}^{ix}}=\frac{2(2-\cos x)}{5-4\cos x}+\frac{2\sin x}{5-4\cos x}\mathrm{i}$$$$Z_1+Z_2=\frac{3}{5-4\cos x}$$

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