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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 real axis

C

`z` lies on the unit circle

D

None of these

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The correct Answer is:
B
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MODERN PUBLICATION-COMPLEX NUMBERS-Multiple Choice Questions (Level-II)
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  2. The points z(1),z(2),z(3),z(4) in complex plane are the vertices of a ...

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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. The locus of the point satisfying the condition amp. ((z-1)/(z+1))=(pi...

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  5. If the imaginary part of (2z+1)/(iz+1) is -2, then the locus of the po...

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  6. If |z| lt 4, then |iz+3-4i| is less than :

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  7. The equation not representing a circle is given by

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  9. If omega is an imaginary cube root of unity, then the value of (1)/(1+...

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  10. In complex plane, the equation |z+barz|=|z-barz| represents:

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

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  12. If |z(1)|=|z(2)|=|z(3)|=1 and z(1)+z(2)+z(3)=0 , then z(1),z(2),z(3) a...

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  13. (cos2theta+isin2theta)^(-5)(cos3theta-isin3theta)^(6)(sintheta-icosthe...

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  14. If z(1)=9y^(2)-4-10ix, z(2)=8y^(2)+20i, where z(1)=z(2) , then z=x+iy ...

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  15. If 1+x^(2)=sqrt(3)x, then sum(n=1)^(24)(x^(n)-(1)/(x^(n)))^(2) equals

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  16. If |z(1)|=|z(2)|=|z(3)|=|z(4)|, then the points representing z(1),z(2)...

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

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  18. If alpha,beta are two complex numbers such that |alpha|=1, |beta|=1, t...

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  19. If ((a+ib)^(2))/(a-ib)-((a-ib)^(2))/(a+ib)=x+iy, then x equals

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  20. If alpha is the nth root of unity then 1+2alpha+3alpha^(2)+..............

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