A) 1
B) - 1
C) i
D) - i
Correct Answer: D
Solution :
\[|z|\,|\omega |\,=1\] ......(i) and \[arg\,\left( \frac{z}{\omega } \right)=\frac{\pi }{2}\,\,\,\Rightarrow \,\,\frac{z}{\omega }=i\] Þ \[\left| \frac{z}{\omega } \right|=1\] .....(ii) From equation (i) and (ii) \[|z|\,=\,|\omega |\,=1\] and \[\frac{z}{\omega }+\frac{{\bar{z}}}{{\bar{\omega }}}=0;\,\,\,z\bar{\omega }+\bar{z}\omega =0\] \[\bar{z}\omega =-z\bar{\omega }=\frac{-z}{\omega }\bar{\omega }\,\omega \]; \[\bar{z}\omega =-\,i\,|\omega {{|}^{2}}=-i.\].You need to login to perform this action.
You will be redirected in
3 sec