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Question

If amp(z1z+1)=π3,Then z represent a point on

A
a circle
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B
a straight line
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C
an ellipse
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D
a hyperbola.
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Solution

The correct option is A a circle
|z1z+1|=k represents a circle if k>0 and k1
If k=1
Then
|z1z+1|=1
Represents a straight line perpendicular to x axis.
That is arg(z1z+1)=0
Hence for
arg(z1z+1)0 it will represent an arc of a circle.
Hence
arg(z1z+1)=π3 represents an arc of a circle.

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