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Home » Live Through This: The Remnant That Changed Everything—A Mind-Blowing Discovery! - inBeat

Live Through This: The Remnant That Changed Everything—A Mind-Blowing Discovery! - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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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...
Subtract: \( (u^4 + 0u^3 + 0u^2) - (u^4 - 2u^3 + 2u^2) = 2u^3 - 2u^2 \...
Bring down: \( +0u + 3 \), now divide \( 2u^3 \div u^2 = 2u \)
Multiply: \( 2u(u^2 - 2u + 2) = 2u^3 - 4u^2 + 4u \)

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