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Question Number 108678 by Rasikh last updated on 18/Aug/20

Answered by abdomsup last updated on 18/Aug/20

$$dontexistlet{x}_n={\left(\frac{1}{n}\right)}^i$$$${lim}_{n\to +\mathrm{\infty }}{x}_n=o^{i}but$$$$x_n=e^{iln\left(\frac{1}{n}\right)=e^{-iln\left(n\right)}=cos\left(lnn\right)+isin\left(lnn\right)}$$$$butcos\left(lnn\right)andsin\left(lnn\right)havent$$$$anylimit$$$$$$

Answered by Her_Majesty last updated on 18/Aug/20

$$z={re}^{i\theta }\wedge r⩾0\wedge \theta \in \mathbb{R}\Rightarrow z^i=r^i{e}^{-\theta }=\frac{1}{e^{\theta }}{e}^{ilnr}$$$$thisisdefinedfor\theta \in \mathbb{R}\wedge r\ne 0$$$$\Rightarrow$$$$0^{i}isnotdefined$$

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