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If z(1)=1+2i, z(2)=2+3i, z(3)=3+4i, then...

If `z_(1)=1+2i, z_(2)=2+3i, z_(3)=3+4i`, then `z_(1),z_(2)` and `z_(3)` represent the vertices of a/an.

A

equilateral triangle

B

right angled triangle

C

isosceles triangle

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Clearly, `z_(2)` is the mid-point of the segment joining `z_(1)` and `z_(3)`. So, the points are collinear.
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Section I - Solved Mcqs
  1. If |z+barz|+|z-barz|=2, then z lies on

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  2. The closest distance of the origin from a curve given as Abarz+barAz+A...

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  3. If z(1)=1+2i, z(2)=2+3i, z(3)=3+4i, then z(1),z(2) and z(3) represent ...

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  4. If z(1) and z(2) are two of the 8^(th) roots of unity such that arg(z(...

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  5. The number of roots of the equation z^(15)=1 satisfying |"arg"(z)| le ...

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  6. If z(1),z(2),……………,z(n) lie on the circle |z|=R, then |z(1)+z(2)+………...

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  7. Q. Let z1 and z2 be nth roots of unity which subtend a right angle at...

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  8. The complex number z1,z2 and z3 satisfying (z1 - z3)/(z2 - z3) = ( 1 -...

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  9. Let omega = - (1)/(2) + i (sqrt3)/(2), then the value of the determina...

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

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  11. Let z1, z2 be two complex numbers represented by points on the circle ...

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  12. If z lies on unit circle with center at the origin, then (1+z)/(1+barz...

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  13. If |z1-1|<1, |z2-2|<2,|z3-3|<3 then |z1+z2+z3|

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  14. Complex numbers z(1) and z(2) lie on the rays arg(z1)=theta and arg(z1...

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  15. If z is a complex number satisfying |z|^(2)-|z|-2 lt 0, then the value...

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  16. |z - i | <= 2 and z0 = 5 + 3i then max. value of |iz+z0| is :

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  17. If |z|= "max"{|z-2|,|z+2|}, then

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  18. if |(z-6)/(z+8)|=1, then the value of x in R, where z=x+i|{:(-3,2i,2+i...

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  19. If |z-1|+|z+3|<=8, then the range of values of |z-4| is

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  20. The equation |z-i|+|z+i|=k, k gt 0 can represent an ellipse, if k=

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