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 polar coordinates is set as a problem in the list of examples. examples
The computation of the phase \(\phi\) requires some care:
\[ \phi = \arctan(y/x), \mod 2\pi, \text{for}\, x > 0 \]
\[ \phi = \arctan(y/x) + \pi, \mod 2\pi, \text{for}\, x < 0 \]
The case \(x=0\) does not occure in the problem.