What contours will allow the integral to equal 0

[dla]

Homework Statement

Determine the contours, C, that will follow Cauchy Integral Theorem so that \large \oint \frac{exp(\frac{1}{z^{2}})}{z^{2}+16} dz =0

Homework Equations

The Attempt at a Solution

The curve can't include z=±4i and z=0 but how do I come up with a curve that does not include those points? Am I just suppose to look for the domain?

 

[haruspex]

The curve can't include z=±4i and z=0

You're certainly OK if it does not include any of those, but maybe by including some combination of them you would still get zero. Not sure whether the question expects you to consider that.