Complex numbers are not vectors.
It could be presented as vector (or as matrix).
Complex numbers are just a way to have a powerful tool for polynomials algebra.
Really, when we talk about "i", we talk about polynomial "x^2+1=0".
And when we use polynomials, we usually use complex numbers, and interpret 'em like frequency (in transfer function) or angular (polar system) or something else.
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Yes, you're right. It's just simple and useful to present our complex number like a vector. You can easily understand how to work with it this way. But they were ctreated to expand defenition of number.