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Question

If three complex numbers z1,z2 and z3 satisfy z1z3z2z3=1i32, then the triangle formed by z1,z2 and z3 is

A
scalene
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B
right-angled isosceles
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C
equilateral
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D
obtuse-angled isosceles
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Solution

The correct option is C equilateral
z1z3z2z3=1i32z1z3z2z3=eiπ/3(1)

Now using the rotation concept we get
z1z3z2z3=|z1z3||z2z3|eiπ/3(2)
comparing (1) and (2), we get
|z1z3|=|z2z3|
and angle between any two sides is 60°
Hence the given triangle is equilateral triangle.

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