z is a unimodular complex number Statement 1: arg(z2+z¯)=argz Statement 2: z¯=cos(argz)−isin(argz)

|z|=1⇒z=cosθ+isinθ where θ=argz  z¯=cosθ−isinθStatement -2 is truearg(z2+z¯)=arg{cos2θ+isin2θ+cosθ−isinθ}=tan−1sin2θ−sinθcos2θ+cosθ=tan−12cos3θ2sinθ22cos3θ2cosθ2 =tan−1tanθ2 =θ2=12argz