0 votes
75 views
in Complex Numbers by (98.9k points)
edited

 (1 – ω – ω2)3 + (1 – ω + ω2)3

1 Answer

0 votes
by (98.9k points)
selected by
 
Best answer

ω is the complex cube root of unity.
ω3 = 1 and 1 + ω + ω2 = 0
Also, 1 + ω2 = -ω, 1 + ω = -ω2 and ω + ω2 = -1
(1 – ω – ω2)3 + (1 – ω + ω2)3
= [1 – (ω + ω2)]3 + [(1 + ω2) – ω]3
= [1 – (-1)]2 + (-ω – ω)3
= 23 + (-2ω)3
= 8 – 8ω3
= 8 – 8(1)
= 0

Related questions

0 votes
1 answer 83 views
asked Sep 11, 2022 in Complex Numbers by Doubtly (98.9k points)
0 votes
0 answers 48 views
asked Sep 11, 2022 in Complex Numbers by Doubtly (98.9k points)
0 votes
1 answer 96 views

Doubtly is an online community for engineering students, offering:

  • Free viva questions PDFs
  • Previous year question papers (PYQs)
  • Academic doubt solutions
  • Expert-guided solutions

Get the pro version for free by logging in!

5.7k questions

5.1k answers

108 comments

537 users

...