Number of ordered pair(s) (x,y) of real numbers such that ${(\mathrm{x}+\mathrm{iy})}^{2023}=\mathrm{x}-\mathrm{iy}$ holds good is

$\begin{array}{l}sZ=x+\dot{y}\Rightarrow \overline{Z}=x-\dot{i}y\\ \text{ so }{Z}^{2023}=\overline{Z}\text{.........(1) }\\ \Rightarrow \left|Z^{2023}\right|=\left|\overline{Z}\right|=\left|Z\right|\Rightarrow |Z{|}^{2023}=|Z|\\ \Rightarrow \left|Z\right|\left(|Z{|}^{2023}-1\right)=0\Rightarrow \left|Z\right|=0\text{ or }\left|Z\right|=1\\ \text{ If }\left|Z\right|=0\Rightarrow \left|Z\right|=0\Rightarrow (0,0)\\ \text{ If }\left|Z\right|=1\Rightarrow Z^{2023}=\overline{Z}\\ \text{ From }\left(1\right)\\ \Rightarrow Z{Z}^{2023}=Z\overline{Z}\Rightarrow Z^{2024}=|Z{|}^2\Rightarrow Z^{2024}=1\\ \Rightarrow 2024\text{ Value of }Z\therefore \text{ Total }=2025\end{array}$