[tex]e^{i\pi}=-1[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]e^{i\frac{\pi}{2}}=i[/tex]

but

[tex]e^{i\frac{\pi}{3}}\neq-1[/tex]

I know there are infinitely many solutions here, but I would expect the third result should include -1 as the cube root of itself. However [tex]e^{\pm ix}=cos(x)\pm{isin(x)}[/tex] would not seem to give -1 for any solution for [tex]x=\frac{\pi}{3}[/tex]. Where am I going wrong here?

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# Euler's identity

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