• Support PF! Buy your school textbooks, materials and every day products Here!

Kudos to whoever can explain this

  • Thread starter Calixto
  • Start date
16
0
Kudos to whoever can explain this!!!

The original question was... how can I show that ... arctan(1/v) = (pi/2) - arctan(v) ???

I understand how to do this the easy way... by forming a right triangle and so on and so forth...

But could someone please explain to me what this is about? Mhill posted this and said it would work, but I don't understand...


if you use the log representation for artan (1/x) and artan (x) so { artan(x)= (2i)^{-1}(log(1+ix)-log(1-ix)) }

and the same replacing x--> 1/x you

get the accurate result.
 

Answers and Replies

Dick
Science Advisor
Homework Helper
26,258
618
If you understand the trig way to do this, then you don't need to do it using complex variables. If you do want to do it that way you'll want to be careful about where the branch cuts are for your definition of log. If you don't know what a branch cut is then don't do it. It's needlessly complicated.
 

Related Threads for: Kudos to whoever can explain this

  • Last Post
Replies
2
Views
764
  • Last Post
Replies
2
Views
769
  • Last Post
Replies
3
Views
924
Replies
13
Views
1K
Replies
8
Views
1K
Replies
1
Views
1K
Replies
19
Views
944
Replies
2
Views
584
Top