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# THe complex numbers z1, z2, z3 satisfying z1-z3/z2-z3 = (1 - v3i)/2 are vertices of triangle which is : a) of area zero b) right angled isosceles c) equilaterald) obtuse angled isosceles

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago
z1 - z3/ z2 - z3 = 1-v3i/2 = e^(-i pi/3)
Therefore, angle between the sides connecting z1,z3 and z2,z3 is pi/3
Also,
| z1-z3| / |z2-z3 | = 1
The two sides are equal in length.
Hence, the triagle is equilateral C)

Thanks & Regards
Bharat Bajaj
IIT Delhi
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

z1 - z3/ z2 - z3 = 1-v3i/2 = e^(-i pi/3)
Therefore, angle between the sides connecting z1,z3 and z2,z3 is pi/3
Also,
| z1-z3| / |z2-z3 | = 1
The two sides are equal in length.
Hence, the triagle is equilateral

Thanks and Regards