Let f be a nonconstant analytic function on the closed bounded region  \{ z \in C ; \mid z \mid \leq 1 \} .Suppose that  \mid f(z) \mid is constant on boundary [i.e there is  k \in R with \mid f(z) \mid =k  \forall z s.t \mid  z  \mid =1 prove that there is  z_0 \in C , \mid z_0 \mid \prec 1  s.t \mid f(z_0 )\mid = 0