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Complex Numbers

A complex number can be represented as a pair of real numbers (cartesian coordinates)
$$z = x + iy$$ or in polar coordinates $$ z = r\,e^{i\, \phi}$$. The phase $$\phi$$ is defined up to a multiple of $$2\,\pi$$

The computation of the phase $$\phi$$ given the cartesion coordinates $$x$$ and $$y$$ requires some care:
$$ r = \sqrt(x^2 + y^2)$$
$$ \phi = $$