Question about the supremum of a set

Question

Let $$X=\sup\left\{\left|\frac{a\sqrt{2}}{2}+b\right|^2+\left|\frac{a\sqrt{2}}{2}-b\right|^2+|b|^2;\;\;(a,b)\in \mathbb{C}^2,\;|a|^2+|b|^2=1\right\}.$$

How can I show that $$X\neq 1\;?$$

Answer 1

With $a=0$ and $b=1$ $\Rightarrow$ $X\geq3$ ?