Which are the difference between polar and coordinate complex numbers?

Polar and coordinase complex numbers are two different ways of represent the same complex numbers. The polar way uses the following formula: Me^(anglej), where M is the modulus of the complex number and can be obtained by Pithagoras´Theorem from the vector coordinates of the number. On the other hand, the angle of the number is calculated by the arctan(vertical coordinate/horizontal coordinate). The cartesian way uses also the modulus and that angle, by in a different way. It is determined by applying Mcos(angle)+jM*sin(angle) And then I would show to the student a numerical example and we would analysed together some different exceptions.