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B
a circle
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C
a pair of lines
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D
none of these
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Solution
The correct option is C a circle |z−1z+1|=k represents a circle if k>0 and k≠1 If k=1 Then |z−1z+1|=1 Represents a straight line perpendicular to x axis. That is arg(z−1z+1)=0 Hence for arg(z−1z+1)≠0 it will represent an arc of a circle. Hence arg(z−1z+1)=π3 represents an arc of a circle.