Mathematics - Complex Number Question with Solution | TestHub

$\left|z_1\right|=\left|z_2\right|=\left|z_3\right|=\dots \dots .=\left|z_n\right|=1$ $\Rightarrow z_1{\bar{z}}_1=z_2{\bar{z}}_2=z_3{\bar{z}}_3=\dots \dots =z_n{\bar{z}}_n=1$ ${\overline{\mathrm{z}}}_1=\frac{1}{\mathrm{z}},{\overline{\mathrm{z}}}_2=\frac{1}{{\mathrm{z}}_2},{\overline{\mathrm{z}}}_3=\frac{1}{{\mathrm{z}}_3},\dots \dots ,{\overline{\mathrm{z}}}_{\mathrm{n}}=\frac{1}{{\mathrm{z}}_{\mathrm{n}}}$ Now, $\left|z_1+z_2+z_3+\dots \dots .+z_n\right|$ $=\left|{\bar{z}}_1+{\bar{z}}_2+\dots \dots +{\bar{z}}_n\right|$ $\left|{\bar{z}}_1+{\bar{z}}_2+{\bar{z}}_3+\dots .+{\bar{z}}_n\right|=\left|\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3}+\dots \dots +\frac{1}{z_n}\right|$