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If w is complex cube root of unity ,show that 1) (2+w+w square)power 3-(1-3w+w square) power 3=65

If w is complex cube root of unity ,show that 1) (2+w+w square)power 3-(1-3w+w square) power 3=65

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Grade:11

2 Answers

Arun
25750 Points
6 years ago
As we know
1+ w+ w2 = 0
& w3 =1
We have to use only these two formulas to find the
answer-
(1+ 1+w+w2)3 - (1+w2 - 3w)3
(1+0)3 - (-w - 3w)3
1 - (-64 w3)
1+ 64
= 65
Hence proved
Hope it helps
 
Sudarshan B K
13 Points
5 years ago
Take n terms of an AP for both Numerator and denominator. 
Cancel all the common terms on both side
Divide both side Numerator and denominator by 2.
Equate coefficient of 'd' in numerator and denominator to 5&20 respectively. 
Solvefor p&q
.

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