Difference between revisions of "Complex number"
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− | 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 | + | 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 number has a '''real part''', denoted by <math>\Re</math>, or simply <math>\mathrm{Re}</math>, and an '''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]]. |
As you can see, complex numbers enable us to remove the restriction of <math>x\ge 0</math> for the domain of <math>f(x)=\sqrt{x}</math>. | As you can see, complex numbers enable us to remove the restriction of <math>x\ge 0</math> for the domain of <math>f(x)=\sqrt{x}</math>. |
Revision as of 11:54, 23 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 number has a real part, denoted by , or simply , and an imaginary part, denoted by , or simply . So, if , we can write , where is the imaginary unit.
As you can see, complex numbers enable us to remove the restriction of for the domain of .
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 w = c+di,
- ,
- ,
Topics
Problems
- AIME