Maharashtra State BoardHSC Science (Electronics) 11th
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If ω is a complex cube root of unity, show that (2 − ω)(2 − ω2) = 7 - Mathematics and Statistics

Sum

If ω is a complex cube root of unity, show that (2 − ω)(2 − ω2) = 7

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Solution

ω is a complex cube root of unity.

∴ ω3 = 1 and 1 + ω + ω2 = 0

∴ ω + ω2 = – 1, 1 + ω = – ω2 and 1 + ω2 = – ω

(2 – ω)(2 – ω2) = 7

= 4 – 2ω2 – 2ω + ω3

= 4 – 2(ω2 + ω) + ω3

= 4 – 2(– 1) + 1

= 4 + 2 + 1

= 7

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