Although one cannot make direct comparisons of two complex numbers,
there are several functions sending a complex number to a real: real and imaginary
parts, module, argument. Via these functions, inequalities can be
established on complex numbers. Geometrically, the set of complex numbers
verifying such an inequality correspond to a region in the complex plane.
This region gives a ``vision'' on the inequality, and helps to understand
the sense of the functions appearing in the inequality.
This online exercise helps you to establish the link between
the inequalities and the geometry of the complex plane.
It can either plot a region and ask you to recognize the
corresponding inequality among a list to choose from, or give an inequality
and ask you to recognize the region it describes.