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Home » Multiply by 3 and Unlock This Sparkling Math Secret That Blows Minds! - ToelettAPP

Multiply by 3 and Unlock This Sparkling Math Secret That Blows Minds! - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Question:** A historian analyzing a manuscript finds an expression involving complex numbers \( z \) and \( w \) satisfying \[ rac{z + w}{z - w} + rac{z - w}{z + w} = 2. \] Determine the value of \( \left| rac{z}{w}

📌 ight| \), assuming \( w

📌 e 0 \) and \( z, w \in \mathbb{C} \).

📌 Solution:** Let \( u = rac{z + w}{z - w} \), so the second term is \( rac{1}{u} \), and the equation becomes:

📌 u + rac{1}{u} = 2.

📌 Multiply by \(u\): \( u^2 - 2u + 1 = 0 \Rightarrow (u - 1)^2 = 0 \Rightarrow u = 1 \).

📌 rac{z + w}{z - w} = 1 \Rightarrow z + w = z - w \Rightarrow 2w = 0 \Rightarrow w = 0.

📌 But this contradicts \( w

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