Electronics Calculations Data Handbook

Appendix 4

Complex number analysis

The standard way to analyse a circuit containing AC quantities at a fixed frequency is to use complex numbers. A complex number has two parts, real and imaginary. The imaginary part is some function of the quantity j (i to pure mathematicians, but that would be confused with current by us), where j represents . This is clearly a ‘nonsense number‘, or at least unquantifiable, yet it has some useful properties:

(A4.1a)

(A4.1b)

(A4.1c)

We use multiplication by j to signify advancing its phase by 90°. Complex ...