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📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Compute $ |z + w|^2 $:

📌 z + w = 4 + 2i \Rightarrow |z + w|^2 = 4^2 + 2^2 = 16 + 4 = 20

📌 Now use the identity:

📌 = |z|^2 + |w|^2 + 2 \operatorname{Re}(z \overline{w}) = 26 + 2 \cdot 5 = 26 + 10 = 36? \quad ext{Wait, contradiction.}

📌 Wait â correction:

📌 From identity:

📌 Substitute known values:

📌 = 26 + 2 \operatorname{Re}(z \overline{w}) \Rightarrow 2 \operatorname{Re}(z \overline{z}) = 20 - 26 = -6 \Rightarrow \operatorname{Re}(z \overline{w}) = -3

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