Difference between revisions of "Real part"
m (→Examples) |
m |
||
Line 27: | Line 27: | ||
* [[Imaginary part]] | * [[Imaginary part]] | ||
+ | |||
+ | [[Category:Algebra]] |
Revision as of 07:00, 17 March 2008
Any complex number can be written in the form where is the imaginary unit and and are real numbers. Then the real part of , usually denoted or , is just the value .
Geometrically, if a complex number is plotted in the complex plane, its real part is its -coordinate (abscissa).
A complex number is real exactly when .
The function can also be defined in terms of the complex conjugate of : . (Recall that if , ).
Examples
- . Note in particular that is not in general a multiplicative function, for arbitrary complex numbers .
Practice Problem 1
Find the conditions on and so that .