A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{2}\]
C) \[\frac{3\pi }{4}\]
D) \[\frac{5\pi }{4}\]
Correct Answer: C
Solution :
Since \[\overline{z}+i\overline{w}=0\Rightarrow \overline{z}=i\overline{w}\] \[\Rightarrow \] \[z=iw\Rightarrow w=-iz\] Also arg\[(zw)=\pi \] \[\Rightarrow \] \[\arg (-i{{z}^{2}})=\pi \] \[\Rightarrow \] \[\arg (-i)+2\arg (z)=\pi \] \[\Rightarrow \] \[-\frac{\pi }{2}+2\arg (z)=\pi \] \[(\because \arg (-i)=-\frac{\pi }{2})\] \[\Rightarrow \] \[2\arg (z)=\frac{3\pi }{2}\] \[\Rightarrow \] \[\arg (z)=\frac{3\pi }{4}\]
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