CameraIcon
CameraIcon
SearchIcon
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 (1ω+ω2)(1ω2+ω4)(1ω4+ω8)(1ω8+ω16) is

A
16
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
17
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
15
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
14
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 16
We have,
ω3=11+ω+ω2=0ω1 ................. (i)
1+ω+ω22ω=2ω i.e. 1ω+ω2=2ω ...................... (ii)
From (i)
1ω2+ω4=1ω2+ω=2ω2 ............. (iii)
1ω4+ω8=1ω+ω2=2ω .............. From (ii)
1ω8+ω16=1ω2+ω=2ω2 ............ From (iii)

Using all above equalities, we get
(1ω+ω2)(1ω2+ω4)(1ω4+ω8)(1ω8+ω16)
=(2ω)(2ω2)(2ω)(2ω2)
=24(ω3.ω3)
2 4=16

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Algebra of Derivatives
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon