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Home » Discover the Ultimate Final Fantasy MTG Card List That’s Taking the Arena by Storm! - DNSFLEX

Discover the Ultimate Final Fantasy MTG Card List That’s Taking the Arena by Storm! - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Convert $ rac{39}{128} $ to denominator 32768:

📌 rac{39}{128} = rac{39 \cdot 256}{128 \cdot 256} = rac{9984}{32768}

📌 Now subtract:

📌 b_5 = rac{9984 - 1521}{32768} = rac{8463}{32768}

📌 Thus, the value of $ b_5 $ is $ oxed{\dfrac{8463}{32768}} $.

📌 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 $

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x^2 + 2 + \frac{1}{x^2} = 25 \Rightarrow x^2 + \frac{1}{x^2} = 23
Now compute $ x^2 + 1 $ and $ x^2 - 1 $:
Let $ A = x^2 + 1 $, $ B = x^2 - 1 $. Then:
\frac{A}{B} + \frac{B}{A} = \frac{(x^2 + 1)^2 + (x^2 - 1)^2}{(x^2 - 1)...
Compute numerator:
Denominator:
\frac{2x^4 + 2}{x^4 - 1} = 2 \cdot \frac{x^4 + 1}{x^4 - 1}
Let’s simplify $ x^4 + 1 $ and $ x^4 - 1 $. Since $ x + \frac{1}{x} =...
x^2 + \frac{1}{x^2} = 23 \Rightarrow x^4 + \frac{1}{x^4} = (x^2 + \fra...
x^4 + 1 = x^4 + \frac{1}{x^4} \cdot x^4 = x^4 + \frac{x^4}{x^4} = x^4...

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