Difference between revisions of "Complex number"
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− | The set of '''complex numbers''' is denoted by <math>\mathbb{C}</math>. The | + | The set of '''complex numbers''' is denoted by <math>\mathbb{C}</math>. The set of complex numbers contains the set <math>\mathbb{R}</math> of the [[real number]]s but is much wider. Every complex numbers has, the '''real part''', denoted by <math>\Re</math> or simply <math>\mathrm{Re}</math>, and the '''imaginary part''', denoted by <math>\Im</math> or simply <math>\mathrm{Im}</math>, so, if <math>z\in \mathbb C</math>, we can write it as <math>z=\Re z+i\Im z</math> where <math>i=\sqrt{-1}</math>. |
The letters <math>z</math> and <math>\omega</math> are usually used to denote complex numbers. | The letters <math>z</math> and <math>\omega</math> are usually used to denote complex numbers. |
Revision as of 11:58, 22 June 2006
The set of complex numbers is denoted by . The set of complex numbers contains the set of the real numbers but is much wider. Every complex numbers has, the real part, denoted by or simply , and the imaginary part, denoted by or simply , so, if , we can write it as where .
The letters and are usually used to denote complex numbers.
Contents
[hide]Operations
- Addition
- Subtraction
- Multiplication
- Division
- Absolute value/Modulus/Magnitude (denoted by ). This is the distance from the origin to the complex number when graphed.
Simple Example
If and ,
- ,
- ,