how find roots for $\frac{\cos(z)}{z}$ for $|z|=2$

Question

I have to find root for this function. My problem is that I only have root on $0$, but this don't allow me to solve related circuital integrate. Which is and why other roots for this function on complex field?

Answer 1

This equation has no roots. The roots of $\frac{\cos z}z$ are the roots of $\cos$, which are the numbers of the form $\frac\pi2+n\pi$ ($n\in\mathbb Z$), none of which has absolute value $2$.