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The complex numbers z1, z2 and z3 satisf...

The complex numbers `z_1, z_2 and z_3` satisfying `(z_1-z_3)/(z_2-z_3) =(1- i sqrt(3))/2` are the vertices of triangle which is (1) of area zero (2) right angled isosceles(3) equilateral (4) obtuse angled isosceles

A

of area zero

B

right-angled isosceles

C

equilateral

D

obtuse-angled isosceles

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`(z_(1)-z_(3))/(z_(2)-z_(3))=(1-isqrt(3))/(2)`

`rArr (z_(1)-z_(3))=e^(-pi//3)(z_(2)-z_(3))`.
`rArr bar(CA)` is obtained by rotating `bar(CB)` through `pi//3` in clockwise sense.
`rArr` CA=CB and `angleAOB=pi/3`
`rArr triangleABC` is an equilateral triangle.
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