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Question

# Assertion :Let z1,z2,z3 be distinct complex numbers & ω3=1,ω≠1If z+ωz2+ω2z3=0 then z1,z2,z3 are the vertices of an equilateral triangle. Reason: If z3−z1=(z2−z1)e−1π/3 then z1,z2,z3 are vertices of an equilateral triangle.

A
Both (A) & (R) are individually true & (R) is correct explanation of (A).
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B
Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
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C
(A) is true (R) is false.
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D
(A) is false (R) is true.
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Solution

## The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A).Subtracting z1(1+ω+ω2)=0from z1+z2ω+ω2z3=0 we get(z2−z1)+ω(z3−z1)=0or z3−z1=−ω2(z2−z1)=ei(π+4π3)−(z2−z3)or z3−z1=(z2−z1)eiπ3∴z1,z2,z3 from an equilateral triangle.

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