# Determining position of pole

i would like to know how to determine if pole of given function is inside a circle of radius 2? for example let us take this function $$f(z)=1/\cos z$$ We have poles at $$z=\pm \pi/2, \pm 3\pi/2, \pm 5\pi/2, \dotsc$$ So which of these poles should be considered for a circle whose radius is 2.

• the ones in the circle: $\pm \pi/2$ – james1395 Apr 28 '16 at 10:53
• That depends on where the center of the circle is. – Henning Makholm Apr 28 '16 at 11:39

You only have to compute the modules and see if they are less than $2$.
For exemple $|\pm \frac{\pi}{2}|<2$ since it is well known that $3<\pi<3,5$.
However the other singularities are not in the disk because the module is greater than $2$.