In mathematics, the absolute value (or modulus) |a| of a real number a is a's numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3.
Generalizations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.
For any real number a the absolute value or modulus of a is denoted by | a | (a vertical bar on each side of the quantity) and is defined as
Since, the complex numbers are not ordered, the definition given above for the real absolute value cannot be directly generalized for a complex number. However the identity given in equation 
:
:can be seen as motivating the following definition.
The graph of the absolute value function for real numbers.
The absolute value of a complex number z is the distance r from z to the origin. It is also seen in the picture that z and its complex conjugate z have the same absolute value.
No comments:
Post a Comment