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Home » This value is achievable when $ x = y = z $, so the minimum is - DNSFLEX

This value is achievable when $ x = y = z $, so the minimum is - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \[ a^2 - b^2 = 0 \quad \text{(1)} \]

📌 \[ 2ab = -2 \quad \text{(2)} \]

📌 From (1): \( a^2 = b^2 \Rightarrow a = b \) or \( a = -b \)

📌 Try \( a = b \):

📌 Then (2): \( 2a^2 = -2 \Rightarrow a^2 = -1 \) — not possible in reals.

📌 Try \( a = -b \):

📌 Let \( b = -a \), then (2): \( 2a(-a) = -2a^2 = -2 \Rightarrow a^2 = 1 \Rightarrow a = \pm 1 \)

📌 If \( a = 1 \), \( b = -1 \), then \( (a + bi)^2 = (1 - i)^2 = 1 - 2i + i^2 = 1 - 2i - 1 = -2i \) ✅

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