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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-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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