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 = {ʹ 2 A : ʹ > 0, ʹ(1) = 1}. For each a 2 A, the C*-algebra numerical range is defined by V (a) := {ʹ(a) : ʹ 2 S}. We prove that if V (a) is a disc with center at the origin, then ka+ak = ka ? ak.