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CIIM 2014 Problem 5

Source:

August 9, 2016
CIIMCIIM 2014undergraduateComplex Variable

Problem Statement

A analityc function f:C→Cf:\mathbb{C}\to\mathbb{C} is call interesting if f(z)f(z) is real along the parabola Re(z)=(Im(z))2Re (z) = (Im (z))^2.
a) Find an example of a non constant interesting function. b) Show that every interesting function ff satisfy that f′(−3/4)=0.f'(-3/4) = 0.
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