1. The problem statement, all variables and given/known data How would one go about finding the fixed points of e^z, where z is complex (i.e. all z s.t. e^z = z)? 2. Relevant equations Nothing. 3. The attempt at a solution I've considered all the relevant formulas (de Moivre's forumla, power series, z = re^i*theta, ...). For some reason, I'm just not getting the solution. I feel that this is going to be really obvious, and I'm not sure why I'm not getting it. Thanks.