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If z=x+iy and w=(1-iz)/(1+iz) , then |w|...

If `z=x+iy` and `w=(1-iz)/(1+iz)` , then `|w|=1` implies that, in the complex plane

A

z lies on the imaginary axis

B

z lies on the unit circle

C

z lies on the real axis

D

none of these

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The correct Answer is:
C
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HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
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  3. If z=x+iy and w=(1-iz)/(1+iz) , then |w|=1 implies that, in the comple...

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

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

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

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

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

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

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

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

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  12. If z(1)=8+4 i, z(2)=6+4 i and arg ((z-z(1))/(z-z(2)))=(pi)/(4) then z ...

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  13. For positive integers n(1) and n(2) the value of the expression (1+i...

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  14. If |{:(6i,-3i,1),(4,-3i,-1),(20,3,i):}|=x+iy, then :

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  15. The value of the sum sum(n=1) ^(13) (i^(n)+i^(n+1)), where i = sqrt( -...

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  16. If omega is an imaginary cube root of unity than (1+omega-omega^(2))^(...

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  17. 4+5(-(1)/(2)+(i sqrt(3))/(2))^(334)+3(-(1)/(2)+(i sqrt(3))/(2))^(365)=

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  18. If z(1),z(2),z(3) are complex numbers such that : |z(1)|=|z(2)|=|z(3)|...

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  19. Let z(1) and z(2) be n^(th ) roots of unity which subtend a right angl...

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  20. Let omega=-(1)/(2)+i (sqrt(3))/(2), then the value of |[1,1,1],[1,-...

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