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

Prove that 11+2ω+12+ω11+ω=0, Where ω is cube root of unity.

Open in App
Solution

11+2ω+12+ω11+ω
=1ωω2+11ω211+ω [ Since 1+ω+ω2=0]
=ω3ωω2+11ω211+ω [ Since ω3=1]
=ω21ω+11ω211+ω
=ω2(1+ω)+11ω211+ω
=2+ω21ω211+ω [ Since ω3=1]
=1ω1ω211+ω [ Since 1ω=2+ω2]
=11+ω11+ω
=0.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Domestic Electric Circuits
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon