Hello, everybody! 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!