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Home » \(\omega^4 = \omega \cdot \omega^3 = \omega(-1) = -\omega\) - Abu Waleed Tea

\(\omega^4 = \omega \cdot \omega^3 = \omega(-1) = -\omega\) - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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lpha^4 + 3 = -4 + 3 = -1 = a(1+i) + b = a + ai + b
Equating real and imaginary parts:
Real: \( a + b = -1 \)
Imaginary: \( a = 0 \)
Wait â imaginary part gives \( a = 0 \)? But then from real: \( b =...
Now try \( u = eta = 1 - i \):
eta^2 = (1 - i)^2 = 1 - 2i + i^2 = 1 - 2i - 1 = -2i
eta^4 = (-2i)^2 = 4i^2 = -4
eta^4 + 3 = -1 = a(1 - i) + b = a - ai + b
Imaginary part: \( -a = 0 \Rightarrow a = 0 \), then \( b = -1 \)

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