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

Complex Logarithm

  • Thread starter soothsayer
  • Start date
  • #1
422
3

Homework Statement


find -Ln(1-e(i[tex]\theta[/tex]) (in terms of theta)

(this is me just skipping the part of the problem I know and going straight to what I can't figure out)

Homework Equations


ln(z) = ln(rei[tex]\theta[/tex])=Ln(r) + ln(ei[tex]\theta[/tex]) = Ln(r) + i[tex]\theta[/tex]

The Attempt at a Solution


I don't really know how to break this logarithm up into real and complex parts, the two ways I considered were

= -(Ln(1-1) + i[tex]\theta[/tex])
but that ends up with Ln(0) which blows up to infinity and doesn't make sense in this problem.

= -(Ln(1) + i[tex]\theta[/tex])
but this is just -i[tex]\theta[/tex] which leaves only an imaginary part, and the problem implies there is a real logarithmic solution as well.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
250
hi soothsayer! :smile:

(have a theta: θ :wink:)

you need to express 1 - e in Cartesian form, a + ib :wink:
 

Related Threads on Complex Logarithm

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
13
Views
727
  • Last Post
Replies
1
Views
594
  • Last Post
Replies
3
Views
452
  • Last Post
Replies
5
Views
1K
Replies
3
Views
3K
Replies
4
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
5
Views
1K
Top