Complex number: Difference between revisions
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== Simple Example == | == Simple Example == | ||
If <math>z=a+bi</math> and <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> | ||
* <math>|z|=\sqrt{a^2+b^2}</math> | * <math>|z|=\sqrt{a^2+b^2}</math> | ||
* <math>\mathrm{Re}( | * <math>\mathrm{Re}(w)=c</math>,<math>\mathrm{Im}(w)=d</math> | ||
* <math>| | * <math>|w|=\sqrt{c^2+d^2}</math> | ||
* <math>z+ | * <math>z+w=(a+c)+(b+d)i</math> | ||
* <math>z- | * <math>z-w=(a-c)+(b-d)i</math> | ||
== Topics == | == Topics == | ||
Revision as of 17:51, 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.
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 
,
,
,
,
,
