If {z_1} and {z_2} are two complex numbers sa | vedclass

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Question

(c)Given $\left| {\frac{{{z_1} + {z_2}}}{{{z_1} - {z_2}}}} ight| = 1$==> $\frac{{{z_1} + {z_2}}}{{{z_1} - {z_2}}} = \cos 	heta + i\sin 	heta $(

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Zero or purely imaginary

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(c)Given $\left| {\frac{{{z_1} + {z_2}}}{{{z_1} - {z_2}}}} ight| = 1$==> $\frac{{{z_1} + {z_2}}}{{{z_1} - {z_2}}} = \cos 	heta + i\sin 	heta $(say)
==> $\frac{{{z_1}}}{{{z_2}}} = \frac{{1 + \cos 	heta + i\sin 	heta }}{{ - 1 + \cos 	heta + i\sin 	heta }} = - i\cot \frac{	heta }{2}$
which is zero, if $	heta = n\pi (n \in I),$ and is otherwise purely imaginary.

If ${z_1}$ and ${z_2}$ are two complex numbers satisfying the equation $\left| \frac{z_1 +z_2}{z_1 - z_2} \right|=1$, then $\frac{{{z_1}}}{{{z_2}}}$ is a number which is

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