Problem 1806 (difficulty: 9/10)

Call an entire function \(\displaystyle f\) ``interesting'', if \(\displaystyle f(z)\) is real along the parabola \(\displaystyle \re z=(\im z)^2\).

(b) Prove that if \(\displaystyle f\) is an interesting function then \(\displaystyle f'(-3/4)=0\).

(a) Show an example for a non-constant interesting function.

CIIM 2014, Costa Rica

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