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Let $f$ be an analytic function defined on $D = \{ z\in \mathbb{C}\colon |z| <1\}$. Then $g \colon D\to \mathbb{C}$ is analytic if

  1. $g(z) = f( \bar{z}) $ for all $z\in D$
  2. $g(z) = \overline{(f (z))}$, for all $z\in D$
  3. $g(z) = \overline{(f (\bar{z}))} $ for all $z\in D$
  4. $g(z) =\bar{i} f (z )$ for all $z\in D$

How can I solve this problem? Please help me anyone.

1 Answers 1