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For any complex number z , find the mini...

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

A

0

B

1

C

2

D

4

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C
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State true or false for the following. For any complex number z, the minimum value of |z| + |z-1| is 1 .

State ture or false for the following. (i) The order relation is defined on the set of complex numbers. (ii) Multiplication of a non-zero complex number by -i rotates the point about origin through a right angle in the anti-clockwise direction.(iiI) For any complex number z, the minimum value of |z|+|z-1| is 1. (iv) The locus represent by |z-1|= |z-i| is a line perpendicular to the join of the points (1,0) and (0,1) . (v) If z is a complex number such that zne 0" and" Re (z) = 0, then Im (z^(2)) = 0 . (vi) The inequality |z-4|lt |z-2| represents the region given by xgt3. (vii) Let z_(1) "and" z_(2) be two complex numbers such that |z_(1)+z_(2)|= |z_(1)+z_(2)| ,then arg (z_(1)-z_(2))=0 . 2 is not a complex number.

If z is a complex number,then find the minimum value of |z|+|z-1|+|2z-3|

OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Chapter Test
  1. If z lies on the circle |z-1|=1, then (z-2)/z is

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  2. If a gt 0 and the equation |z-a^(2)|+|z-2a|=3, represents an ellipse, ...

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

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  4. Find the greatest and the least value of |z1+z2| ifz1=24+7ia n d|z2|=6...

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

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  6. If k gt 1, |z(1)| lt k and |(k-z(1)barz(2))/(z(1)-kz(2))|=1, then

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  7. If |z-i|=1 and arg (z) =theta where 0 lt theta lt pi/2, then cottheta-...

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  8. If Re(z)<0 then the value of (1+z+z^2+.....+z^n) cannot exceed

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  9. Let z(1),z(2),z(3) be three complex numbers satisfying 1/z(1)+1/z(2)+1...

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  10. a and b are real numbers between 0 and 1 such that the points z1 =a+ i...

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  11. If omega is a cube root of unity, then find the value of the following...

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  12. If a ,b ,c and u ,v ,w are the complex numbers representing the vertic...

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  13. If z=re^i theta then |e^(iz)| is equal to:

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  14. If a complex number z lies in the interior or on the boundary of a cir...

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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 z(1),z(2),z(3) be vertices of an equilateral triangle occurig in th...

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  17. Let z be a complex number satisfying |z-5i|<=1 such that amp(z) is min...

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  18. If |z-25i| lt= 15. then |"maximum " arg(z) - "minimum " arg(z)| equals

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  19. Let z be a complex number (not lying on x-axis) of maximum modulus suc...

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  20. The maximum distance from the origin of coordinates to the point z sat...

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