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Home » $ d_3 = d_4 $: 1 - Midis

$ d_3 = d_4 $: 1 - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \[ (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i \]

📌 \[ 4 \cdot i = 4i \]

📌 \[ \text{Discriminant} = 2i - 4i = -2i \]

📌 Now, compute \( \sqrt{-2i} \). Let \( \sqrt{-2i} = a + bi \), then:

📌 \[ (a + bi)^2 = a^2 - b^2 + 2abi = -2i \]

📌 \[ a^2 - b^2 = 0 \quad \text{(1)} \]

📌 \[ 2ab = -2 \quad \text{(2)} \]

📌 From (1): \( a^2 = b^2 \Rightarrow a = b \) or \( a = -b \)

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