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**Physics-is-Phun** This is a homework problem for my Mathematical Physics course, where we're learning complex numbers and so on right now. I didn't see the subject over in the Physics site, and I wasn't quite sure which category this belonged in over here, so please move it if it if it's more appropriate somewhere else!

Anyway, on to the problem.

**Either solve for z in the equation **$\displaystyle e^z = 0$**, or show that this cannot be done.**

I attempted to show that it could not be done by taking the natural logarithm of both sides:

$\displaystyle ln(e^z) = ln(0)$

$\displaystyle z = ln(0)$

I then concluded by saying that, since you cannot take the natural logarithm of 0, the problem is unsolvable, or z is undefined, or you cannot solve for z.

I wanted to make sure that my reasoning is correct, or if I am actually wrong and it can be done (though I don't want the solution handed to me, if I'm wrong- just point me in the right direction, please!).

Thank you in advance!