Chapter 2.17, Problem 25MP

(a) Show that $\overline{\cos z}=\cos \bar{z}$.

(b) Is $\overline{\sin z}=\sin \bar{z}$?

(c) If $f(z)=1+iz,is\overline{f(z)}=f(\bar{z})$?

(d) If $f(z)$ is expanded in a power series with real coefficients show that $\overline{f(z)}=f(\bar{z})$.

(e) Using part (d) verify, without computing its value, that is real.