Class 9 Homework-

Let \(f(z) = z+ \sum_{n=2}^\infty a_nz^n ,|z| <1\). If \(\sum_{n=2}^\infty |a_n| \le 1\), then prove that \(f\) is one-one,

(i) without using Rouche’s theorem and

(ii) using Rouche’s theorem.




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