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IF A1,A2,A3,...,A BE N-TH ROOTS OF THE UNITY THEN THE VALUE OF (A1/3-A1+A2/3-A2+A3/3-A3+...+A /3-A )= A)N/3 N-1 B)N-1/3 N-1

 


IF A1,A2,A3,...,A BE N-TH ROOTS OF THE UNITY THEN THE VALUE OF (A1/3-A1+A2/3-A2+A3/3-A3+...+A/3-A)=


A)N/3N-1 


B)N-1/3N-1 


 

Grade:11

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Please find the answer to your question below
GivenA1,A2,A3,...,ABE N-TH ROOTS OF THE UNITY
Then(A1/3-A1+A2/3-A2+A3/3-A3+...+A/3-A)=
taking 1/3 common from above we get
(A1+A2+......+An)/3-(A1+A2+......+An)=0
because according to the properties of nth roots of unity
Sum of nth roots of unity is zero.

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