A) zero
B) real and positive
C) real and negative
D) purely imaginary or zero
Correct Answer: D
Solution :
\[\frac{{{z}_{1}}+{{z}_{2}}}{{{z}_{1}}-{{z}_{2}}}.\frac{{{\overline{z}}_{1}}+{{\overline{z}}_{2}}}{{{z}_{1}}-{{z}_{2}}}=\frac{2i\,\operatorname{Im}({{z}_{1}}.\,{{\overline{z}}_{2}})}{|{{z}_{1}}-{{z}_{2}}|}\] \[\Rightarrow \]Purely imaginary when\[\operatorname{Im}({{z}_{1}}.\,{{z}_{2}})\ne 0\]or zero.You need to login to perform this action.
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