Revision as of 15:25, 4 September 2008 by Mfrankos (Talk)

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) $

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