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Question

Let A =23eiπ6, 23eiπ2, 23ei5π6 three points forming a triangle ABC in the plane then triangle ABC is

A
Equilateral
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B
Isosceles
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C
Scalene
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D
Right angled
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Solution

The correct option is A Equilateral
arg(A)=π6
arg(B)=π2
arg(C)=5π6
arg(A)arg(B)=2π3
arg(B)arg(C)=4π3
arg(C)arg(A)=2π3
as all differences are in multiple of 2π3,ABC is equilateral triangle

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