Let $z_1,z_2,\dots,z_n\in\Bbb{C}$ be distinct and $w_1,w_2,\dots,w_n\in\Bbb{C}$ be arbitrary. Suppose $f, g$ are two polynomials of degree less than $n$ such that $$f(z_j)=w_j,\qquad g(z_j)=\bar{w}_j \qquad\text{for $1\leq j\leq n$}.$$ Define $\Omega(z)=\prod_{j=1}^n(z-z_j)$. The following puzzles me.

Question 1.Is this true? $$\sum_{k=1}^n\frac{\vert f^{\prime}(z_k)\vert^2}{\vert \Omega^{\prime}(z_k)\vert^2}\leq \sum_{k=1}^n\frac{\vert g^{\prime}(z_k)\vert^2}{\vert\Omega^{\prime}(z_k)\vert^2}.$$

**EDIT.** I'm sorry, one of the conditions was missing. To give credit, I'll leave the question as it stands and ask the correct one below.

Question 2.What if we insist that $f$ and $g$ have equal degrees?

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