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 12:54, 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.
Operations
- Addition
- Subtraction
- Multiplication
- Division
- Absolute value/Modulus/Magnitude (denoted by
). This is the distance from the origin to the complex number when graphed.
). This is the distance from the origin to the complex number when Simple Example
If 
and w = c+di,
,
,
,
,
Topics
Problems
- AIME
