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Home » 4v + \frac83 < 25 - Parker Core Knowledge

4v + \frac83 < 25 - Parker Core Knowledge

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 But this contradicts $ \operatorname{Re}(z \overline{w}) = 5 $ from (2). So we must reevaluate:

📌 Wait â there is an error in interpretation. The expression $ z \overline{w} + \overline{z} w = 2 \operatorname{Re}(z \overline{w}) $, and this is given as 10, so $ \operatorname{Re}(z \overline{w}) = 5 $.

📌 But from the identity:

📌 |z + w|^2 = |z|^2 + |w|^2 + 2 \operatorname{Re}(z \overline{w}) = 26 + 2(5) = 26 + 10 = 36

📌 But $ |z + w|^2 = |4 + 2i|^2 = 16 + 4 = 20

📌 e 36 $. Contradiction.

📌 Thus, the given conditions are inconsistent unless we recheck the problem. But since the question asks to find $ \operatorname{Re}(z \overline{w}) $, and gives $ z \overline{w} + \overline{z} w = 10 $, then regardless of the other data,

📌 \operatorname{Re}(z \overline{w}) = rac{1}{2} (z \overline{w} + \overline{z} w) = rac{10}{2} = 5

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