Geometrical representation of complex numbers


[2. Mathematical elements.]Geometrical representation of complex numbers.Complex numbers can be geometrically represented on the two dimensional Cartesian coordinate system, assigning the real part to the xaxis and the imaginary part to the yaxis. The complex number z=a+ib is represented as the vector from the origin to the point (a,b). In this geometrical interpretation of complex numbers some operations have an intuitive meaning.
The following formula, known as Euler's formula, defines an interesting relation between complex numbers and trigonometric functions: e ^{i x} = cos x + i sin x.
