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If omega=(z)/(z-(i)(3)) and |omega|=1,...

If `omega=(z)/(z-(i)(3))` and `|omega|=1`, the z lies on

A

a circle

B

an ellipse

C

a parabola

D

a straight line

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Verified by Experts

The correct Answer is:
D
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HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
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  2. If the cube root of unity are 1,omega,omega^(2), then the roots of the...

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  3. If omega=(z)/(z-(i)(3)) and |omega|=1, the z lies on

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  4. If w=alpha+ibeta, where beta ne 0 and z ne 1, satisfies the condition ...

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  5. The value of sum(k=1) ^(10)( sin "" ( 2kpi )/( 11) + i cos "" ( 2kpi )...

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  6. If z^(2)+z+1=0 then sum(r=1)^(6)(z^(r)+(1)/(z^(r)))^(2)=

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  7. If |z+4| le 3, then the maximum value of |z+1| is

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  8. The values of x and y which satisfy the equation ((1+i) x-2 i)/(3+i)...

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  9. The complex plane of z=x+iy, which satisfies the equation |(z-5i)/(z+5...

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  10. If z=((sqrt(3))/(2)+(i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5), then:

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  11. The points z(1),z(2),z(3),z(4) in complex plane are the vertices of a ...

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  12. If z=x+iy and w=(1-iz)/(1+iz) , then |w|=1 implies that, in the comple...

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  13. If z(1),z(2),z(3) represent the vertices of an equilateral triangle su...

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  14. If z(1), z(2), z(3) are three complex numbers in A.P., then they lie o...

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  15. If z(1) and z(2) are two non-zero complex numbers such that |z(1)+z(2)...

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  16. sin x+i cos 2 x and cos x-i sin 2 x are conjugate to each other for,

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  17. If 1, omega, omega^(2) are the three cube roots of unity and alpha, be...

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  18. The complex number (1+2i)/(1-i) lies in

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  19. If z ne 0 and Re z=0 then

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  20. If z ne 0 and arg z=(pi)/(4), then

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