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Home » But question says "fill the entire solution" — total volume is 729. - Esdistancia

But question says "fill the entire solution" — total volume is 729. - Esdistancia

📅 March 17, 2026 👤 scraface

Mar 17, 2026

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📌 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

📌 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.

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