What is the Difference Between Log, ln, arg, and Arg in Complex Analysis?

[sweetvirgogirl]

my complex analysis book uses all three of them...

although i know the difference between log and ln, I'm kinda clueless about Log ... any ideas?

 

[devious_]

It's probably the principle value of log. I'm sure your book has it mentioned somewhere.

 

[Rach3]

Just in case:
http://en.wikipedia.org/wiki/Multivalued_function

 

[TD]

my complex analysis book uses all three of them...

although i know the difference between log and ln, I'm kinda clueless about Log ... any ideas?

In my textbook, log was used to denote the 'old' logarithm for real values only, and Log for the complex logarithm (i.e. Log(z) = log(r) + i*phi, with phi the phase, if I recall correctly).

 

[sweetvirgogirl]

In my textbook, log was used to denote the 'old' logarithm for real values only, and Log for the complex logarithm (i.e. Log(z) = log(r) + i*phi, with phi the phase, if I recall correctly).

let me tell you how my textbook defines certain terms ...

log z = ln |z| + i * arg z
Log z = ln |z| + i * Arg z

now consider this example:
log (1+ i * 3^(1/2)
now the value I would get is ... ln |1+ i * 3 ^(1/2)| + i ( pi/3 + 2 n pi)
which simplifies to ln 2 + i (pi/3 +2 n pi)

now the answer in the back of the book is log 2 + i (pi/3 +2 n pi)
and this is not the first time they have done it ... so i don't think it's a typo ...

lol ... mind explaning how they replaced ln 2 with log 2??
thanks!

 

[sweetvirgogirl]

another thing ...
why do they always use n2pi (n = 0, , 1, -1, 2, -2...)??
coz the values in case of tangent give the same value for n * pi

 

[sweetvirgogirl]

hmmm... bump?

 

[shmoe]

log z = ln |z| + i * arg z
Log z = ln |z| + i * Arg z

Your task is to now look up how they define arg and Arg. Most likely, Arg will denote some 'principle branch' and be a single valued function while arg is the multivalued version.

... mind explaning how they replaced ln 2 with log 2??

In advanced textbooks (=beyond intro calculus) "log" usually denotes the base e logarithm, i.e. the "ln" on your calculator. They probably explain this somewhere in your text.