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Question Number 92424 by Jidda28 last updated on 06/May/20

$$\mathrm{If}2\mathrm{x}-0\mathrm{i}={\varrho }^{\pi \mathrm{i}}$$$$\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}$$

Commented by mathmax by abdo last updated on 06/May/20

$$2x-oi=e^{\pi i}\Rightarrow 2x=-1\Rightarrow x=-\frac{1}{2}because{e}^{i\pi }=cos\pi +isin\pi =-1$$$$ifwewantallsolution2x=e^{i\pi +2ik\pi }=e^{i(2k+1)\pi }\Rightarrow$$$$x_k=\frac{1}{2}{e}^{i(2k+1)\pi }kfromZ$$

Commented by Jidda28 last updated on 06/May/20

$$\mathrm{thank}\mathrm{you}\mathrm{so}\mathrm{much}\mathrm{sir}$$

Commented by mathmax by abdo last updated on 07/May/20

$$youarewelcome.$$

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