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If z\neq{0} and z moves such that \\\mathrm{\left | z - 2 \right | = \left | z + 2 \right |}, then \mathrm{|arg(z)|}  equals

Option: 1

\pi


Option: 2

\frac{\pi}{2}


Option: 3

\frac{\pi}{4}


Option: 4

None of these


Answers (1)

best_answer

As we have learnt

|z - z1| = |z - z2| is the equation of perpendicular of bisector of AB, where A(z1) and B(z2)

 

Now

The given equation is the perpendicular bisector of two points A(2+0i) and B(-2+0i), meaninf perpendicular bisector of (2,0) and (-2,0),which is y axis. Hence z will lie on y axis, so it’s argument will be  \frac{\pi}{2} or -\frac{\pi}{2}

So mod of argument will always be \frac{\pi}{2}

So the correct option is (b)

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