| Line 10: | Line 10: | ||
<math>j^4 = 1</math> | <math>j^4 = 1</math> | ||
| − | == | + | == Addition == |
<math>(a+bj)+(c+dj) = (a + c) + (c + d)j</math> | <math>(a+bj)+(c+dj) = (a + c) + (c + d)j</math> | ||
| + | |||
| + | <math>(1+3j)+(2+4j) = (3 + 7j)</math> | ||
| + | |||
| + | == Subtraction == | ||
| + | <math>(a+bj)-(c+dj) = (a-c)+(b-d)j</math> | ||
| + | |||
| + | <math>(1+3j)-(2+4j) = (-1 - 4j)</math> | ||
| + | |||
| + | == Multiplication == | ||
| + | <math>(a+bj)*(c+dj) = (ac-bd)+(ad+bc)j</math> | ||
| + | |||
| + | <math>(1+3j)*(2+4j) = (-10 + 10j)</math> | ||
== division == | == division == | ||
| − | <math>(a+bj)/(c+dj) = | + | <math>(a+bj)/(c+dj) = ((a+bj)*(c-dj))/((c+dj)*(c-dj)) = ((ac+bd)+(-ad+bc)j)/(c^2+d^2)</math> |
| + | |||
| + | <math>(1+3j)/(2+4j) = (0.7 + 0.1j)</math> | ||
Revision as of 16:25, 4 September 2008
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) $
