Complex Analysis Entire Functions

[bballife1508]

Let f(z) be an entire function such that |f(z)| less that or equal to R whenever R>0 and |z|=R.

(a)Show that f''(0)=0=f'''(0)=f''''(0)=...

(b)Show that f(0)=0.

(c) Give two example of such a function f.

 

[snipez90]

Hint: look back through your old post history. I already explained one tool you could use to approach these problems.