If a > e prove that the equation a*z^n=e^z has n solutions (counting multiplicities) inside of the circle |z|=1.© BrainMass Inc. brainmass.com March 4, 2021, 6:04 pm ad1c9bdddf
Proof. Let f(z)=a*z^n and g(z)=-e^z. On the circle C: |z|=1, we have
This proves that a given equation has n solutions inside of a given circle.