CircleHard
Question
A complex number z is said to be unimodular if |z| = 1. Suppose z1 and z2 are complex numbers such that 
is unimodular and z2 is not unimodular. Then the point z1 lies on a :
is unimodular and z2 is not unimodular. Then the point z1 lies on a :Options
A.circle of radius 2
B.circle of radius √2
C.straight line parallel to x-axis
D.straight line parallel to y-axis
Solution
= 1 ⇒ |z1 − 2z2|2 = |2 − z1
|2⇒ (z1 − 2z2)(
− 
) = (2 − z1)(2 − z2)⇒ |z1|2 + 4|z2|2 − 4 − |z1|2 |z2|2 = 0
⇒ 4(|z2|2 − 1) − |z1|2 (|z2|2 − 1) = 0
⇒ |z1|2 − 4 = 0⇒|z1| = 2 is a circle of radius 2 and centre at origin.
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