A) \[\arg (z-1)=2\arg (z)\]
B) \[2\arg (z)=\frac{2}{3}\arg ({{z}^{2}}-z)\]
C) \[\arg (z-1)=\arg (z+1)\]
D) \[\arg (z)=2\arg (z+1)\]
Correct Answer: A
Solution :
Clearly, \[|z-1|\,\,=1\]represents a circle with centre at\[(1,\,\,0)\] and radius 1. Let \[P(z)\] be any point on it. Then, \[\arg (z-1)=\angle XCP=\theta \] [say] \[\therefore \] \[\arg (z)=\angle XOP=\frac{\theta }{2}\] Hence,\[\arg (z-1)=2\arg (z)\]You need to login to perform this action.
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