w1 = and w2 =(w1)^2
show that [/FONT][/COLOR]
I am able to find (w1)^2
But that is all I can do
$(x-w_1y)(x-w_2y) = x^2 - \color{red}{(w_1+w_2)}xy + \color{blue}{w_1w_2}y^2$w1 = - 1/2 + (√3/2)i and w2 =(w1)^2
show that x^2 +xy+y^2=(x-w1y)(x-w2y)
$\color{red}{w_1 + w_2} = w_1 + w_1^2 = \left(\dfrac{-1+i\sqrt{3}}{2}\right) + \left(\dfrac{-2-2i\sqrt{3}}{4}\right) = \dfrac{-2+2i\sqrt{3}-2-2i\sqrt{3}}{4} = \color{red}{-1}$
$\color{blue}{w_1w_2} = w_1 w_1^2 = \left(\dfrac{-1+i\sqrt{3}}{2}\right) \cdot \left(\dfrac{-2-2i\sqrt{3}}{4}\right) = \dfrac{2 +2i\sqrt{3}-2i\sqrt{3}+6}{8} = \color{blue}{1}$