This chapter has covered just enough about complex numbers to enable us to talk about the discrete Fourier transform.
Manipulations of complex numbers in Matlab and Octave are illustrated in §I.1.
To explore further the mathematics of complex variables, see any textbook such as Churchill  or LePage . Topics not covered here, but which are important elsewhere in signal processing, include analytic functions, contour integration, analytic continuation, residue calculus, and conformal mapping.
De Moivre's Theorem