Is the following statement is true or false?

Question

Is the following statement is true or false ?

the function $f(z) = sin z$ is not conformal on the on the infinite stripsD ={${z\in C :|Rez|< \pi}/{2}$}

i thinks this statement is true as$ f'(z) =cosz$ as $f'(z) = 0$ when$ z = \pi/{2}$

so my answer is this is true....

Pliz verifies im correct or not ?

thanks in advance....

Answer 1

Yes, it is conformal on that strip, since $f'(z)=\cos(z)$ and $\cos(z)\neq0$ when $|\operatorname{Re}z|<\frac\pi2$.