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-2-b-2-c-2-ab-bc-c-Kindly-help-me-out-Thank-you-

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