Question

(1+omega) ³+(1+omega²) ³​

Answer 1

Answer:

your answer is as follows

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Step-by-step explanation:

$to \: find : \\ (1 + ω) {}^{3} + (1 + ω {}^{2} ) {}^{3} \\ where \: ω \: is \: cube \: root \: of \: unity \\ \\ we \: know \: that \\ 1 + ω + ω {}^{2} = 0 \\ \\ ω {}^{3} = 1$

$(1 + ω) {}^{3} + (1 + ω {}^{2} ) {}^{3} \\ \\ = (1 + ω) {}^{3} + ( - ω) {}^{3} \\ \\ = 1 + ω {}^{3} + 3ω + 3ω {}^{2} - ω {}^{3} \\ \\ = 1 + 3ω + 3ω {}^{2} \\ \\ = ( - ω - ω {}^{2} ) + 3ω + 3ω {}^{2} \\ \\ = 2ω + 2ω {}^{2} \\ \\ = 2(ω + ω {}^{2} ) \\ \\ = 2( - 1) \\ \\ = - 2$