But as shown, this leads to inconsistency with $ |z + w|^2 = 20 $ and $ |z|^2 + |w

February 22, 2026

But as shown, this leads to inconsistency with $ |z + w|^2 = 20 $ and $ |z|^2 + |w

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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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