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Question

If ω is a cube root of unity, then

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Solution

If w is a cube root of unity then

A]. 1+w+w2=0|1+w+w2|=0

B]. w3+(w3)2=1+12=2

C]. Since the modulus of the complex number and its conjugate are equal so
|a+bw+cw2||a+bw2+cw|=1

D]. 1+wn+w2n=0 [if n in not a integral multiple of 3]
=3 [if n is integral multiple of 3]

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