A) Positive real
B) Negative real
C) Zero or purely imaginary
D) None of these
Correct Answer: C
Solution :
Given \[\left| \frac{{{z}_{1}}+{{z}_{2}}}{{{z}_{1}}-{{z}_{2}}} \right|=1\]Þ \[\frac{{{z}_{1}}+{{z}_{2}}}{{{z}_{1}}-{{z}_{2}}}=\cos \theta +i\sin \theta \](say) Þ \[\frac{{{z}_{1}}}{{{z}_{2}}}=\frac{1+\cos \theta +i\sin \theta }{-1+\cos \theta +i\sin \theta }=-i\cot \frac{\theta }{2}\] which is zero, if \[\theta =n\pi (n\in I),\] and is otherwise purely imaginary.You need to login to perform this action.
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