If w is the cube root of unity. Prove that (1 - w + w²)⁶ + (1 + w - w²)⁶ = 128
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Answer:
128
Step-by-step explanation:
Concept:
If ω is a cube root of unity
then
1+ω+ω²=0
and
ω³ = 1
( 1 - ω+ ω² )⁶ + ( 1 + ω - ω² )⁶
=( - ω - ω )⁶ + ( - ω² - ω² )⁶
=( - 2ω )⁶ + ( - 2ω² )⁶
=64 +64
=128
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