Difference between revisions of "Complex number"
ComplexZeta (talk | contribs) (→Simple Example) |
|||
Line 31: | Line 31: | ||
* [[Roots of unity]] | * [[Roots of unity]] | ||
* [[Geometry with complex numbers]] | * [[Geometry with complex numbers]] | ||
+ | |||
+ | == Problems == | ||
+ | *AIME | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=392620#p392620 1984 #8] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=421338#p421338 1985 #3] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=458040#p458040 1988 #11] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=436603#p436603 1989 #14] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=459508#p459508 1990 #10] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=430620#p430620 1992 #10] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=53847#p53847 1994 #8] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=394743#p394743 1994 #13] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=394478#p394478 1995 #5] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=394249#p394249 1996 #11] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=393654#p393654 1997 #11] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=393661#p393661 1997 #14] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=392484#p392484 1998 #13] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=392227#p392227 1999 #9] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=385894#p385894 2000 Alternate #9] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=378395#p378395 2002 #12] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=378129#p378129 2004 #13] | ||
+ | ** [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=368277#p368277 2005 Alternate #9] | ||
+ | |||
=== See also === | === See also === |
Revision as of 09:32, 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 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 w = c+di,
- ,
- ,
Topics
Problems
- AIME