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.