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In some sense, 「complex plane」( its alias is 「Gaussian plane」) to visually express the complex numbers (＝ a ＋ bi) also is a Columbus egg-like idea.
But we should pay attention that a direct product of complex planes is apparently equal to a 4-dimensional manifold.
Because a 4-dimensional manifold has remarkably different characters from phenomena in other dimensions ( as 「2 ＋ 2 ＝ 2 × 2」holds？).
