Difference between revisions of "Complex number"
ComplexZeta (talk | contribs) (→Simple Example) |
ComplexZeta (talk | contribs) (→Simple Example) |
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== Simple Example == | == Simple Example == | ||
− | If <math>z=a+bi</math> and <math>w=c+di</math>, | + | If <math>z=a+bi</math> and <math>w = c+di</math>, |
* <math>\mathrm{Re}(z)=a</math>,<math>\mathrm{Im}(z)=b</math> | * <math>\mathrm{Re}(z)=a</math>,<math>\mathrm{Im}(z)=b</math> |
Revision as of 18:51, 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 a real part, denoted by
or simply
, and a 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
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
,
,
,