Algebra> THe complex numbers z1, z2, z3 satisfying...

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

Samir Madan , 11 Years ago

Grade 12

2 Answers

bharat bajaj

Last Activity: 11 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

Approved

Rishi Sharma

Last Activity: 5 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