If you have two complex numbers in a vector, couldn't that be represented as a point in 4d?
Just trying to understand why quantum physics uses complex matrices instead of real matrices of double the length.
2026-05-17 01:08:49.1778980129
What is the difference between a complex vector of length 2 and a real vector of length 4?
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I'd recommend checking out this post - it discusses the difference between vectors and scalars, and notions of multiplication and division over these objects.
In essence, complex numbers are 2-dimensional values just like 2D real-valued vectors, but the multiplication defined over them becomes particularly useful in certain contexts (i.e. quantum mechanics, among many others), and no such multiplication is generally defined on $\mathbb{R}^2$.
I particularly enjoy the quote in pjs36's response, "Yes, we could define multiplication and division in $\mathbb{R}^2$ using $\mathbb{C}$, but it would be dishonest."