Prove inequality between two $\sup$s in $\mathbb{C}$ and in $\mathbb{R}$

Question

Consider $A=\{z \in \mathbb{C}: |z|<1\}$ and $B=\{x \in \mathbb{R}: |x|<1\}$ and $N \in \mathbb{N}$. How can I prove the following inequality?

$$\sup_{z \in A} \frac{|z^{N}|}{|1-z|}\geq \sup_{x \in B}\frac{|x^{N}|}{|1-x|}$$

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I tried using $|1-z|\geq |1-|z||$ but it doesn't seem the proper way to do it.

Answer 1

Supremum on the left side is taken over a bigger set (since $B \subset A$). Thus, the supremum on the left is greater.