If ${\mathrm{z}}_1=2\mathrm{i}-3\text{ and }{\mathrm{z}}_2=\mathrm{x}-\mathrm{iy}$ and  ${\mathrm{z}}_2-{\mathrm{z}}_1=0$ then find x, y values are

$\begin{array}{l}\mathrm{x}-\mathrm{iy}-(2\mathrm{i}-3)=0\\ \mathrm{x}-\mathrm{iy}-2\mathrm{i}+3=0\\ (\mathrm{x}+3)+\mathrm{i}(-\mathrm{y}-2)=0+\mathrm{i}\left(0\right)\end{array}$
Comparing coefficients
$$\begin{gathered} \mathrm{x}+3=0 \\ \mathrm{x}=-3 \end{gathered}$$          $$\begin{gathered} -\mathrm{y}-2=0 \\ -\mathrm{y}=2 \\ \mathrm{y}=-2 \end{gathered}$$