Mathematics - Complex Number Question with Solution | TestHub

$z_1{\bar{z}}_1=z_2{\bar{z}}_2=\dots .=z_n{\bar{z}}_n=1$ $\Rightarrow {\overline{\mathrm{z}}}_1=\frac{1}{{\mathrm{z}}_1},{\overline{\mathrm{z}}}_2=\frac{1}{{\mathrm{z}}_2},{\overline{\mathrm{z}}}_3=\frac{1}{{\mathrm{z}}_3},\dots \dots ,{\overline{\mathrm{z}}}_{\mathrm{n}}=\frac{1}{{\mathrm{z}}_{\mathrm{n}}}$ $\therefore \left|z_1+z_2+\dots .+z_n\right|-\left|\frac{1}{z_1}+\frac{1}{z_2}+\dots .+\frac{1}{z_n}\right|$ $=\left|z_1+z_2+\dots +z_n\right|-\left|{\bar{z}}_1+{\bar{z}}_2+\dots .+{\bar{z}}_n\right|=0$