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If ω is a complex cube root of unity, find the value of (1+ω2)3

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Question

If ω is a complex cube root of unity, find the value of (1 + ω2)3

Sum
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Solution

ω is a complex cube root of unity
∴ ω3 = 1 and 1 + ω + ω2 = 0

Also, 1 + ω2 = - ω, 1 + ω = -  ω2 and ω + ω2 = – 1

(1 + ω2)= (- ω)3 = - ω3 = - 1

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Chapter 3: Complex Numbers - EXERCISE 3.3 [Page 42]

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