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I want a clear explanation for this question which is from complex numbers

I want a clear explanation for this question which is from complex numbers

Question Image
Grade:12

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
ok we have
x^5 - 1 = (x-1)(x^4+x^3+x^2+x+1) = 0
now as the w is a root of the ablove equation we have
\omega^4 + \omega^3+\omega^2+\omega + 1 = 0 \quad and \quad \omega^4 = 1/\omega
log_2|1 + \omega^3+\omega^2+\omega -1/\omega| = log_2|1 +\omega^4+ \omega^3+\omega^2+\omega -2\omega^4| = log_2|-2\omega^4|
log_2|-2\omega^4| = 1+4log_2|\omega|

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