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The definition of a ''complex analytic function'' is obtained by replacing, in the definitions above, "real" with "complex" and "real line" with "complex plane". A function is complex analytic if and only if it is [[Holomorphic function|holomorphic]] i.e. it is complex differentiable. For this reason the terms "holomorphic" and "analytic" are often used interchangeably for such functions.<ref>{{cite book |quote=A function ''f'' of the complex variable ''z'' is ''analytic'' at point ''z''<sub>0</sub> if its derivative exists not only at ''z'' but at each point ''z'' in some neighborhood of ''z''<sub>0</sub>. It is analytic in a region ''R'' if it is analytic at every point in ''R''. The term ''holomorphic'' is also used in the literature to denote analyticity |last=Churchill |last2=Brown |last3=Verhey |title=Complex Variables and Applications |publisher=McGraw-Hill |year=1948 |isbn=0-07-010855-2 |page=[https://archive.org/details/complexvariable00chur/page/46 46] |url-access=registration |url=https://archive.org/details/complexvariable00chur/page/46 }}</ref>
In complex analysis, a function is called analytic in an open set "U" if it is (complex) differentiable at each point in "U" and its complex derivative is continuous on "U". <ref>{{Cite book |last= Gamelin |first= Theodore W. |title=Complex Analysis |publisher=Springer |year=2004|isbn= 9788181281142}}</ref>
== Examples ==
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