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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

None of these

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The correct Answer is:
C
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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|

MCGROW HILL PUBLICATION-COMPLEX NUMBERS -SOLVED EXAMPLES LEVEL 1
  1. The inequality |z-4| lt |z-2| represents

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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