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Home » He Deserves The Best—These Anniversary Gifts for Him Will Blow His Mind! - AMAZONAWS

He Deserves The Best—These Anniversary Gifts for Him Will Blow His Mind! - AMAZONAWS

He Deserves The Best—These Anniversary Gifts Will Blow His Mind!

📅 March 11, 2026 👤 scraface
Mar 11, 2026
He Deserves The Best—These Anniversary Gifts for Him Will Blow His Mind!

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📌 Question: A museum curator catalogs a 3D artifact with three vertices of a regular octahedron at $ (1, 0, 0) $, $ (-1, 0, 0) $, and $ (0, 1, 0) $. Find the coordinates of the fourth vertex, given all coordinates are integers.
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📌 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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