If 2z1/3z2 is purely imaginary then, | Z1 – z2/ z1 + z2| =

a) 3/2

b) 1

c) 2/3

d) 4/9

Dear Pooja,

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Aman Bansal

Askiitian Expert

Hi Pooja,

If 2z1/3z2 is purely imaginary, then z1/z2 is purely imaginary.

Which means z1/z2 + z1'/z2' = 0 -------------(where ' denotes the complex conjugate)

So z1z2' + z1'z2 = 0--------------------(1)

Now | (z1-z2)/(z1+z2) |^2 = (z1-z2)(z1'-z2')/(z1+z2)(z1'+z2') = {|z1|^2 + |z2|^2}/{|z1|^2 + |z2|^2} = 1 --------[By using (1)].

So the given expression = 1. Option (2).

Best Regards,

Ashwin (IIT Madras).