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Question

If |z1|=|z2|=|z3|=1 and z1+z2=0, then z1,z2,z3 are the vertices of a triangle which is

A
Right angled
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B
Isosceles
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C
Obtuse angled
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D
Equilateral
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Solution

The correct option is A Right angled
Consider an unit circle centered at origin.
Then z1,z2,z3 are points on its circumference.
Now
z1+z2=0
Hence
z1=z2
Thus z2 is the diametrically opposite point to z1.
Hence
z1z2 is the diameter.
Now since z3 is also a point on the circumference of the circle, it is therefore at a unit distance from the origin.
Now z1z2 being the fixed diameter, and the third vertice being on the circumference ultimately gives infinite right angled triangles with z1z2 as hypotenuse and right angled at z3

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