Numerical Range in C*-Algebras

Let a be a c*-algebra with unit 1 and let s be the state space of a, i.e., s = {φ element of a*: φ ≥ 0, φ (1) =1}. for each a element of a, the c*-algebra numerical range is defined by v (a) := {φ(a) : φ element of s}. we prove that if v (a) is a disc with center at the origin, then ||a+a*|| = ||a-a*||.