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The vector space $\mathbb C / \mathbb R$ does not have a preferred basis. Among the two bases ${1, i}$ and ${1, -i}$ and i}$, there is no reason to prefer one over the other. The choice of one of these amounts to a choice of an orientation for the plane. 1 [made Community Wiki] The vector space$\mathbb C / \mathbb R$does not have a preferred basis. Among the two bases${1, i}$and${1, -i}\$ and there is no reason to prefer one over the other. The choice of one of these amounts to a choice of an orientation for the plane.