Hello, everybody!(adsbygoogle = window.adsbygoogle || []).push({});

I'm a Maths/Physics student at Ecuador. Sorry if my English sucks, i'll try to do my best... Some fellow Physics buddy asked me if there was a way to fin a complex number that would be equal to its exponential... it is a very simple question to understand, but not to easy to prove or disprove (at least not for me, and i've tried it for a day).

So, this is what I got:

z = Ln (z)

and we would have to solve these equations:

ln r = rcos O

O = rsen O

that would be hard to solve algebraically, I guess... I wouldn't want a numeric aproach, so maybe there is a more ellegant way to find an example of disprove the hypothesis. (I already tried Taylor expansions)

Well, please try to give some ideas on the subject.

Have a good one!

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# A very interesting question on complex variable

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