Difference between revisions of "Complex number"
Line 1: | Line 1: | ||
− | 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> | + | 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 <math>z=\mathrm{Re}(z)+i\mathrm{Im}(z)</math> where <math>i</math> is the [[imaginary unit]]. |
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 12:05, 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 where is the imaginary unit.
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 ,
- ,
- ,