For how many ordered pairs $(a,b)$ of complex numbers does the system of equations $\begin{cases} x^2y-x=a\\ xy^2+y=b \end{cases}$ have exactly one complex number solution?

**Details and assumptions**

A complex number solution is an ordered pair of complex numbers $(x,y)$ that satisfies both equations.

Clarification: $a, b, x$ and $y$ are all complex numbers. As an explicit example, $(x,y) = (i, i)$ is a solution to $(a,b) = (-2i, 0 )$.

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