Teaching CSIR NET Mock Test Series Mathematical Science Complex Analysis Analytic Functions

Let S1 = {z ∈ ℂ : |z| = 1}. For which one of the following functions f does there exist a sequence of polynomials in z that uniformly converges to f on S1 ?

1
f(z) = z̅ 
2
f(z) = Re(z)
3
f(z) = ez
4
f(z) = |z + 1|2
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