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If |z|=1 and omega=(z-1)/(z+1) (where z ...

If `|z|=1` and `omega=(z-1)/(z+1)` (where `z in -1`), then Re`(omega)` is

A

0

B

`-(1)/(|z+1|^(2))`

C

`|(z)/(z+1)|(1)/(|z+1|^(2))`

D

`(sqrt(2))/(|z + |^(2))`

Text Solution

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A
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MCGROW HILL PUBLICATION-COMPLEX NUMBERS -SOLVED EXAMPLES LEVEL 1
  1. If z ne 0 be a complex number and "arg"(z)=-pi//4, then

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  2. Let za n dw be two non-zero complex number such that |z|=|w| and a r g...

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  3. If |z|=1 and omega=(z-1)/(z+1) (where z in -1), then Re(omega) is

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  4. Let z and w be two complex numbers such that |Z| <= 1, |w|<=1 and |z -...

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  5. The complex numbers z = x + iy which satisfy the equation |(z-5i)/(z+5...

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  6. The inequality |z-4| lt |z-2| represents

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  7. If z1 and z2 are two complex numbers such that |(z1-z2)/(z1+z2)|=1, th...

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  8. For any complex number z , find the minimum value of |z|+|z-2i|dot

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  9. If x=2+ 5i then the value of x^3-5x^2+33x-19 is

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

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

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

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

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

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

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

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

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

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

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