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Home » This Bow Wallpaper Will Transform Your Room in Seconds—Don’t Miss It! - Professionaloutdoormedia

This Bow Wallpaper Will Transform Your Room in Seconds—Don’t Miss It! - Professionaloutdoormedia

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 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 \( 0 + 0 = 0 \).

📌 Alternatively, interpret as sum over all **solutions** (with multiplicity or not)? But in algebraic contexts like this, unless specified, we consider distinct roots or with multiplicity. But multiplicity doesn't affect real part — each root contributes its real part once in evaluation, but the real part function is defined per root. However, in such symmetric cases, we sum over distinct roots unless told otherwise.

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