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

If `z=x+iy` and `w=(1-iz)/(z-i)`, then `|w|=1` implies that in the complex plane (A)`z` lies on imaginary axis (B) `z` lies on real axis (C)`z` lies on unit circle (D) None of these

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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MCGROW HILL PUBLICATION-COMPLEX NUMBERS -SOLVED EXAMPLES LEVEL 1
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  3. If z=x+iy and w=(1-iz)/(z-i), then |w|=1 implies that in the complex ...

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  4. The real part of z = (1)/(1-cos theta + i sin theta) is

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  5. If the imaginary part of (2z + 1)/(iz + 1) is -4, then the locus of th...

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  6. Show that the area of the triagle on the argand plane formed by the co...

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  7. If omega is a complex cube root of unity, then a root of the equation ...

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  8. Let z1 and z2 be two non - zero complex numbers such that z1/z2+z2/z...

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  9. If (1+x+x^2)^n=a0+a1x+a2x^2++a(2n)x(2n), find the value of a0+a6++ ,n ...

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  10. Let z = |(1,1-2i,3+5i),(1+2i,-5,10i),(3-5i,-10i,11)|, then

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  11. if (x+i y)^(1/3) = a+ib then (x/a) + (y/b) equals to

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  12. If z epsilon C, the minimum value of |z| + |z-i| is attained at

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  13. For all complex numbers z1, z2 satisfying |z1| =12 and |z2-3-4i|=5, ...

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  14. If z lies on the circle |z-1|=1, then (z-2)/z is

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  15. If 1, omega, ......,omega^(n-1) are the n^(th) roots of unity,then va...

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  16. If omega = "cos"(pi)/(n) + "i sin" (pi)/(n), then value of 1 + omega +...

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

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  18. The locus of the center of a circle which touches the circles |z-z1|=a...

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  19. If |z^2-1|=|z|^2+1, then z lies on (a) a circle (b) the imaginar...

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  20. If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+...

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