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Home » Gobi Desert Map Exposed: Uncover Secrets of Asia’s Mysterious Desert in Seconds! - Abbey Badges

Gobi Desert Map Exposed: Uncover Secrets of Asia’s Mysterious Desert in Seconds! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question: Let $ z $ and $ w $ be complex numbers such that $ z + w = 4 + 2i $ and $ z \overline{w} + \overline{z} w = 10 $. If $ |z|^2 + |w|^2 = 26 $, find $ \operatorname{Re}(z \overline{w}) $.

📌 Solution: We are given:

📌 $ z + w = 4 + 2i $

📌 $ z \overline{w} + \overline{z} w = 10 $

📌 $ |z|^2 + |w|^2 = 26 $

📌 We are to find $ \operatorname{Re}(z \overline{w}) $.

📌 Note that $ z \overline{w} + \overline{z} w = 2 \operatorname{Re}(z \overline{w}) $, so from (2):

📌 \operatorname{Re}(z \overline{w}) = 10 \Rightarrow \operatorname{Re}(z \overline{w}) = 5

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