# Real and complex roots

of the equation
z= exp(-z)

could someone possibly point me in the right direction to start this problem?
this area of math is still new to me so please go easy
thanks

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berkeman
Mentor
I moved this thread to the homework section. gmans, what do you mean by the equation that you have written? What is "exp" representing?

arildno
Homework Helper
Gold Member
Dearly Missed
Probably, he means:
$$z=e^{-z}$$

quasar987
That's a fun problem. I say start by defining z=a+ib where a and b are real numbers and also note z=|z|exp(i$\Phi$) the polar form of z, so that you're looking for the solutions to
$$|z|e^{i\Phi}=e^{-a-ib}$$
And use the fact that two complex numbers are equal iff their modulus are the same and their polar angle are the same up to a difference of $2n\pi$, $n\in\mathbb{Z}$.