Definition of Complex Number
A complex number can be defined as $ j = \sqrt(-1) $
$ j^1 = j $
$ j^2 = -1 $
$ j^3 = -j $
$ j^4 = 1 $
Addition
$ (a+bj)+(c+dj) = (a + c) + (c + d)j $
$ (1+3j)+(2+4j) = (3 + 7j) $
Subtraction
$ (a+bj)-(c+dj) = (a-c)+(b-d)j $
$ (1+3j)-(2+4j) = (-1 - 4j) $
Multiplication
$ (a+bj)*(c+dj) = (ac-bd)+(ad+bc)j $
$ (1+3j)*(2+4j) = (-10 + 10j) $
Division
$ (a+bj)/(c+dj) = ((a+bj)*(c-dj))/((c+dj)*(c-dj)) = ((ac+bd)+(-ad+bc)j)/(c^2+d^2) $
$ (1+3j)/(2+4j) = (0.7 + 0.1j) $
