complex logarithm
The solution of (1) is obtained by using the form , where and ; the result is
Here, the means the usual Napierian or natural logarithm (http://planetmath.org/NaturalLogarithm2) (‘logarithmus naturalis’) of the real number . If we fix the phase angle of so that , we can write
The complex logarithm is defined for all and it is infinitely multivalued e.g. where is an arbitrary integer. The values with are called the of the ; if is real, the value of coincides with .
Title | complex logarithm |
Canonical name | ComplexLogarithm |
Date of creation | 2013-03-22 14:43:11 |
Last modified on | 2013-03-22 14:43:11 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 10 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 32A05 |
Classification | msc 30D20 |
Synonym | natural logarithm |
Related topic | Logarithm |
Related topic | NaturalLogarithm2 |
Related topic | ValuesOfComplexCosine |
Related topic | EqualityOfComplexNumbers |
Related topic | SomeValuesCharacterisingI |
Related topic | UsingResidueTheoremNearBranchPoint |