Let B = {z:|z|<3, Re z + Im z <= 0}
prove that the function f(z) = cosh(1+iz^2)/cos z
is bounded on the set delta B
Could anyone give me a steer on how I should go about solving this?
Many thanks
Graham
I'm not sure to be honest. The approach I have taken is as follows:
|cosh(1+iz^2)/cos z|
= |1/2 (e^(1+iz^2)+e^-(1+iz^2)) / 1/2(e^iz+e^-iz)|
= e^1+|z^2|+e^1+|z^2| / |e^z|+|e^z|
= e^1+|z^2| / e^|z|
When |z|< 3, this equates to e^7
It looks right but I can't find a way to check this.