It's right, assuming you realize that is a set, and not a number.

Note that has simple poles at for all . Thus, find the number of them lying inside the disc and use the residue theorem which says then that, if are those finitely many poles then and since each pole is simple you need only calculate the residue by

(2)use the residue theorem to evaluate

integralc(tanz)dz where c is the positively orientated circle |z|=2

i thought with the residue theorem you had to have a fraction so you could set the bottom to zero and get a singularity. I thought you could change tanz into sinz/cosz and set cosz to zero. but thats wrong

any help appreciated on either question

thanks