A) equal to 1
B) less than 1
C) greater than 3
D) equal to 3
Correct Answer: A
Solution :
[a] : Given, \[|{{z}_{1}}|=|{{z}_{2}}|=|{{z}_{3}}|=1\] Now, \[|{{z}_{1}}|=1\Rightarrow |{{z}_{1}}{{|}^{2}}=1\Rightarrow {{z}_{1}}{{\overline{z}}_{1}}=1\] Similarly,\[{{z}_{2}}{{\overline{z}}_{1}}=1,{{z}_{3}}{{\overline{z}}_{3}}=1\] Now, \[\left| \frac{1}{{{z}_{1}}}+\frac{1}{{{z}_{2}}}+\frac{1}{{{z}_{3}}} \right|=1\] \[\Rightarrow \]\[\left| \begin{matrix} \frac{{{z}_{1}}{{\overline{z}}_{1}}}{{{z}_{1}}}+ & \frac{{{z}_{2}}{{\overline{z}}_{2}}}{{{z}_{2}}}+ & \frac{{{z}_{3}}{{\overline{z}}_{3}}}{{{z}_{3}}} \\ \end{matrix} \right|=\left| {{\overline{z}}_{1}}+{{\overline{z}}_{2}}+{{\overline{z}}_{3}} \right|=1\] \[\Rightarrow \]\[\left| {{z}_{1}}+{{z}_{2}}+{{z}_{3}} \right|=1\]
You need to login to perform this action.
You will be redirected in
3 sec
