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📅 May 5, 2026 👤 scraface

May 05, 2026

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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 \( b = -1 \)
So both give \( a = 0 \), \( b = -1 \)
Conclusion: the remainder is constant \( -1 \)
Alternatively, polynomial division confirms:
Divide \( u^4 + 0u^3 + 0u^2 + 0u + 3 \) by \( u^2 - 2u + 2 \)
First: \( u^4 \div u^2 = u^2 \), multiply: \( u^2(u^2 - 2u + 2) = u^4...

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