Solve

This is what I did... I'm not sure if I'm in the right direction about this problem.

I am french so excuse me if my translation in english isn't accurate.

I used the residual theorem.

The integral of is 0. (Cauchy's Theorem).

Poles of order 1 at

Only the pole at z = ia is in the semi-circle drawn above.

Residual at z = ia :

What does cos(ia) represent ? Does that even exist?

If this is totally wrong, then how do I solve this problem?