An imaginary complex number is just a 2D vector-the operations we do on imaginary complex numbers are just regular vector operators-why make such a big deal over it?
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In vector calculus, "'divergence "'is a vector operator that produces a signed scalar field giving the quantity of a vector field's source at each point.
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Note that here, the term " vector " is used two different ways : kets such as are elements of abstract Hilbert spaces, while the vector operator is defined as a quantity whose components transform in a certain way under rotations.
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For example, the scalar product { \ mathbf L } \ cdot { \ mathbf S } of the two vector operators, { \ mathbf L } and { \ mathbf S }, is a scalar operator, which figures prominently in discussions of the spin-orbit interaction.
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