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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) equilateral d) obtuse angled isosceles

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) equilateral
d) obtuse angled isosceles

Grade:12

2 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
10 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
askIITians Faculty
IIT Delhi
Rishi Sharma
askIITians Faculty 646 Points
3 years 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

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