A) 2
B) \[\frac{\sqrt{3}}{4}\]
C) \[\frac{\sqrt{3}}{2}\]
D) None
Correct Answer: D
Solution :
\[{{\left( 1+\frac{1}{z} \right)}^{4}}=1\]\[\Rightarrow \]\[{{(z+1)}^{4}}={{z}^{4}}\]\[\Rightarrow \]\[|z+1|+|z|\] \[\Rightarrow \]\[(z+1)(\overline{z}+1)=z.\overline{z}\Rightarrow z+\overline{z}=-1\]\[\Rightarrow \]\[2\operatorname{Re}(z)=-1\] \[\therefore \]roots of given equation lie on line and so all points collinear.You need to login to perform this action.
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