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Question

The points representing the complex number z for which arg(z2z+2)=π3 lie 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 parabola
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Solution

The correct option is A A circle

Given that arg(z2)arg(z+2)=π3

arg(z2)arg(z+2)=π3

Hence, two fixed points (2,0) and (2,0) subtend an angle of π3 at z.

So, z lies on major arc of a circle whose chord is the line joining (2,0) and (2,0) as shown in the figure.


198767_14600_ans_51e9b15dada14e13a7299672a793ec89.png

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