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The complex number z1,z2 and z3 satisfyi...

The complex number `z_1,z_2 and z_3` satisfying `(z_1 - z_3)/(z_2 - z_3) = ( 1 - i sqrt3)/2` are the vertices of a triangle which is :

A

of area zero

B

right-angled isosceles

C

equilateral

D

obtuse-angle isosceles

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The correct Answer is:
C
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MCGROW HILL PUBLICATION-COMPLEX NUMBERS -EXERCISE LEVEL 1
  1. If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...

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

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

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

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  5. The inequality |z-i| lt |z + i| represents the region

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  6. Show that if iz^3+z^2-z+i=0, then |z|=1

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  7. If x + iy = (1)/(1-cos theta + 2 i sin theta), theta ne 2n pi, n in I,...

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  8. The equation z^3=bar z has

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  9. If z = 5 + t + isqrt(25 - t^(2)), (-5 le t le 5), then locus of z is a...

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  10. If omega is complex cube root of that 1/(a+omega)+1/(b+omega)+1/(c+ome...

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  11. if |z-iRe(z)|=|z-Im(z)| where i=sqrt(-1) then z lies on

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  12. If omega is a complex cube root of unity, then value of expression cos...

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  13. If roots of the equation z^2+ az + b = 0 are purely imaginary then

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  14. The system of equations |z+1-i|=sqrt2 and |z| = 3 has

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  15. If 8iotaz^3+12z^2-18z+27iota=0 then: a. |z|=3/2 b. |z|=2/3 c. |z|=...

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

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  17. If x+iy=3/(2+costheta +i sin theta), then show that x^2+y^2=4x-3

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  18. Suppose z(1), z(2), z(3) represent the vertices A, B and C respectivel...

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  19. Suppose that three points z(1), z(2), z(3) are connected by the relati...

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  20. If the number (z-1)/(z+1) is purely imaginary, then

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