Originally Posted by

**dazed** Hey, I would really appreciate some hints on how to tackle this please:

For a natural number N, let CN be the square with vertices at ±(N + 1

2 )(1 ± i).

Show that there is a constant K so that

maxzeCN | cot(pi*z)| is less than or equal to K.

I know it could help to estimate the value of | cot(pi*z)| separately on each side of the square separately using the fact that

cot(pi*z)= i(exp(i*pi*z) + exp(-i*pi*z))/exp(i*pi*z) - exp(-i*pi*z), but do not know how to go about this.

Thanks.