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Home » Is This the Ultimate Chick-fil-A Merch Collection You’ve Been Hunting Online? - AMAZONAWS

Is This the Ultimate Chick-fil-A Merch Collection You’ve Been Hunting Online? - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 z = \sqrt{2}i, \quad z = -\sqrt{2}i

📌 These are distinct and purely imaginary. The real part of each is 0.

📌 Thus, the sum of the real parts is:

📌 Even though there are four roots? Let's double-check factorization.

📌 z^4 + 4z^2 + 4 = (z^2 + 2)^2 = 0

📌 So indeed, \( (z^2 + 2)^2 = 0 \), so roots are \( z = \pm i\sqrt{2} \), each with multiplicity 2. But the **set of distinct roots** is still two: \( i\sqrt{2}, -i\sqrt{2} \), each included twice. But the problem asks for **the sum of the real parts of all complex numbers \( z \)** satisfying the equation. Since real part is 0 for each, even with multiplicity, the sum is still \( 0 + 0 = 0 \).

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