If for any 2 complex nos. z₁ and z₂, $\left(\left|{\mathrm{z}}_2\right|\ne 1\right)\sqrt{{\mathrm{z}}_1}-\mathrm{i}\sqrt{{\mathrm{z}}_2}=\left|{\mathrm{z}}_2\right|\sqrt{{\mathrm{z}}_1}+\mathrm{i}\left|{\mathrm{z}}_1\right|\sqrt{{\mathrm{z}}_2}$, then which of the following options are correct

$\sqrt{{\mathrm{z}}_1}\left(1-\left|{\mathrm{z}}_2\right|\right)=\sqrt{{\mathrm{z}}_2}\mathrm{i}\left(1+\left|{\mathrm{z}}_1\right|\right)\Rightarrow \frac{\sqrt{{\mathrm{z}}_1}}{\sqrt{{\mathrm{z}}_2}}=$
purely imaginary $\Rightarrow \frac{{\mathrm{z}}_1}{{\mathrm{z}}_2}=$purely real (negative)
$\begin{array}{l}\frac{\sqrt{{\mathrm{z}}_1}}{\sqrt{{\mathrm{z}}_2}}+\frac{\sqrt{{\mathrm{z}}_1}}{\sqrt{\overline{{\mathrm{z}}_2}}}=0\\ \Rightarrow \text{ Also }\sqrt{{\mathrm{z}}_1}-\mathrm{i}\sqrt{{\mathrm{z}}_2}=\sqrt{{\mathrm{z}}_2\overline{{\mathrm{z}}_2}}\sqrt{{\mathrm{z}}_1}+\mathrm{i}\sqrt{{\mathrm{z}}_1\overline{{\mathrm{z}}_1}}\sqrt{{\mathrm{z}}_2}\\ \Rightarrow \left(1-\mathrm{i}\sqrt{{\mathrm{z}}_1{\mathrm{z}}_2}\right)\left(\sqrt{{\mathrm{z}}_1}-\mathrm{i}\sqrt{{\mathrm{z}}_2}\right)=0\\ \Rightarrow {\overline{\mathrm{z}}}_1{\mathrm{z}}_2=-1\text{ or }\frac{{\mathrm{z}}_1}{{\mathrm{z}}_2}=-1\end{array}$