wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If ω is a complex cube root of unity, then the value of the expression 1(2ω)(2ω2)+2(3ω)(3ω2)+...+(n1)(nω)(nω2) is

A
n2(n+1)24n
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
n2(n+1)24+n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
n2(n+1)4n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
n(n+1)24n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A n2(n+1)24n
We know,
(x31)=(x1)(xw)(xw2) (1)
So in the given expression for first term
1(2w)(2w2)=(21)(2w2)(2w2)
=(231) [from equation (1)]
Similarly doing for all terms the expression reduces to
=231+331+431n31
=(13+23....n3)(n1)1 [add and subtract 1]
=n2(n+1)24n

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
What Is a Good Fuel?
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon