Complex Numbers

Let \(a \neq b\) be two non-zero real numbers. Then the number of elements in the set \(X=\left\{z \in \mathbb{C}: \operatorname{Re}\left(a z^{2}+b z\right)=a\right.\) and \(\left.\operatorname{Re}\left(b z^{2}+a z\right)=b\right\}\) is equal to :