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A complex number z is said to be unimodu...

A complex number z is said to be unimodular if `abs(z)=1`. Suppose `z_(1)` and `z_(2)` are complex numbers such that `(z_(1)-2z_(2))/(2-z_(1)z_(2)^_)` is unimodular and `z_(2)` is not unimodular. Then the point `z_(1)` 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 `sqrt(2)`

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The correct Answer is:
C
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VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
  1. A complex number z is said to be unimodular if abs(z)=1. Suppose z(1) ...

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  2. If z is a complex number such that |z|geq2 , then the minimum value...

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  3. Let complex numbers alpha and 1/alpha lies on circle (x-x0)^2+(y-y0)^2...

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  4. Let z be a complex number such that the imaginary part of z is nonz...

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  5. Let z = x + iy be a complex number where x and y are integers. Then...

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  6. If |z|=1a n dz!=+-1, then all the values of z/(1-z^2) lie on a line no...

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  7. If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition tha...

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  8. If |z|=1 and w=(z-1)/(z+1) (where z!=-1), then R e(w) is 0 (b) 1/(|...

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  9. about to only mathematics

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  11. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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  12. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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  13. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  14. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  15. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  16. about to only mathematics

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  17. If z is complex number of unit modulus and argument theta then arg ...

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  18. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+tz(2...

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  19. A particle P starts from the point z0=1+2i , where i=sqrt(-1) . It mov...

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  20. A man walks a distance of 3 units from the origin towards the North-...

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