If w is one of the complex cube roots of unity, show that (a+wb+w^2 c)(a+w^2 b+wc) is equal to (α^2 +b^2 +c^2 −ab−bc−cα). Kindly help me out, Thank you.


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Question Number 183667 by Mastermind last updated on 28/Dec/22

$If w is one of the complex cube$ $roots of unity, show that$ $(a + wb + w^{2} c) (a + w^{2} b + wc) is equal$ $to (α^{2} + b^{2} + c^{2} - ab - bc - c α) .$ $Kindly help me out, Thank you .$
Commented by mr W last updated on 28/Dec/22

$i f y o u k n o w (a + b) (c + d), t h e n y o u c a n$ $a l s o s o l v e t h i s .$
Commented by Frix last updated on 28/Dec/22

$w^{2} = conj w \Rightarrow w^{2} + w = - 1$ $w^{3} = 1$ $Should be easy now .$
Commented by Rasheed.Sindhi last updated on 28/Dec/22

$T y p o s i n y o u r q u e s t i o n a s u s u a l .$ $C o r r e c t e d v e r s i o n :$ $(a + ω b + ω^{2} c) (a + ω^{2} b + ω c)$ $= a^{2} + b^{2} + c^{2} - ab - bc - ca$
Commented by Mastermind last updated on 28/Dec/22

$Thank you sir$ $but i {can}^{'} t see the solution$
Commented by Frix last updated on 28/Dec/22

$Maybe the Master of the Mind is not the$ $Master of the Formulas ?$
Commented by Rasheed.Sindhi last updated on 10/Jan/23
✌️ Share your solution then
Commented by Mastermind last updated on 10/Jan/23

$Smile$ $Anyways, have gotten it BOSS$
Commented by Mastermind last updated on 19/Jan/23

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