\begin{array}{l}{\text { If } \alpha \text { and } \beta \text { are t

1.	\begin{array}{l}{\text { If } \alpha \text { and } \beta \text { are the complex cube roots of } y} \\ {\text { show that }} \\ {\alpha^{2}+\beta^{2}+\alpha \beta=0 .}\end{array}
Answer» α and β are cube roots of unity let α=ω ,β=ω² α²+β²+αβ=ω²+ω⁴+ω³= ω²+ω+1=0 ( because sum of cube roots of unity is zero)

\begin{array}{l}{\text { If } \alpha \text { and } \beta \text { are the complex cube roots of } y} \\ {\text { show that }} \\ {\alpha^{2}+\beta^{2}+\alpha \beta=0 .}\end{array}

Answer»

α and β are cube roots of unity

let α=ω ,β=ω²

α²+β²+αβ=ω²+ω⁴+ω³= ω²+ω+1=0

( because sum of cube roots of unity is zero)