Difference between revisions of "Complex number"
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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.
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 ,
- ,
- ,