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A complex number can be defined as <math>j = \sqrt(-1)</math> | A complex number can be defined as <math>j = \sqrt(-1)</math> | ||
| − | <math>j^1 = j | + | <math>j^1 = j\!</math> |
| − | j^2 = -1 | + | |
| − | j^3 = -j | + | <math>j^2 = -1\!</math> |
| − | j^4 = 1</math> | + | |
| + | <math>j^3 = -j\!</math> | ||
| + | |||
| + | <math>j^4 = 1\!</math> | ||
| + | |||
| + | == Addition == | ||
| + | <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 == | ||
| + | <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> | ||
Latest revision as of 06:39, 5 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)\! $
