Complex numbers


2. Mathematical elements.Some mathematical instruments necessary for a comprehension of quantum mechanics are described: complex numbers, complex functions, derivatives and partial derivatives of complex functions. Complex numbers.
A complex number is a number of the type a+ib where a and
b are real numbers, called respectively the real and the imaginary part,
and i² = 1.
If b=0 then the complex number is also a real number, that is a real
number is a complex number which has no imaginary part.
The four basic operation (addition, subtraction, multiplication and division) between complex numbers are carried out like the corresponding operations on real polynomials, remembering that i² = 1. Some examples:
