Complex Analysis (Residual Theorem).

Solve http://www.cramster.com/Answer-Board...6250001362.gif

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.

http://www.cramster.com/answer-board...5e8d04299e.jpg

http://www.cramster.com/Answer-Board...3750005613.gif

http://www.cramster.com/Answer-Board...5000005092.gif

The integral of http://www.cramster.com/Answer-Board...0000003333.gif is 0. (Cauchy's Theorem).

Poles of order 1 at http://www.cramster.com/Answer-Board...4093750666.gif

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

Residual at z = ia :

http://www.cramster.com/Answer-Board...5937504249.gif

http://www.cramster.com/Answer-Board...2500001241.gif

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

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