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© Physics
Helpline
Physics Helpline
L K Satapathy
Complex Numbers 2
© Physics
Helpline
Physics Helpline
L K Satapathy
Complex Numbers 2
Answer :
Question : A complex number z is said to be unimodular if z = 1.
Suppose and are two complex numbers such that is unimodular
and is not unimodular. Then the point lies on a
(a) straight line parallel to x-axis (b) straight line parallel to y-axis
(c) circle of radius 2 (d) circle of radius
1z 2z1 2
1 2
22z zz z
2z 1z
1 21 2
1 2 1 2
221 1
2 2z zz z
z z z z
2 21 2 1 22 2z z z z
Given that
1 2 1 2 1 2 1 2( 2 )( 2 ) (2 )(2 )z z z z z z z z
2
1 2 1 22 2z z z z
© Physics
Helpline
Physics Helpline
L K Satapathy
Complex Numbers 2
1 1 1 2 1 2 2 2 1 2 1 2 1 1 2 22 2 4 4 2 2z z z z z z z z z z z z z z z z
1 1 2 2 1 1 2 24 4 0z z z z z z z z
1 1 2 2( 4)( 1) 0z z z z
22 2 2 2 2 21 1 1 ( 1) 0z z z z z z
1 1 1 1( 4) 0 4z z z z
z1 lies on a circle of radius 2
1 1 2 2 1 1 2 24 4z z z z z z z z
1 1 2 2 2 2( 1) 4( 1) 0z z z z z z
21 14 2z z
Correct option = (c)
© Physics
Helpline
Physics Helpline
L K Satapathy
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