A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
Lokisan,
I have another complex analysis question for you....what is the integral of 1/z dz if that z is imaginary again....
anonymous
 5 years ago
Lokisan, I have another complex analysis question for you....what is the integral of 1/z dz if that z is imaginary again....

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Laurie, if you mean z is complex, then the integral of 1/z dz is log(z) for a suitable branch cut. Usually we would take Log(z) which is the principle logarithm. Log(z) is the integral to 1/z because it can be shown that the derivative of log(z) is 1/z (sounds circular, but we have to use the Fundamental Theorem of the Calculus). You would have then\[\int\limits_{}^{}\frac{dz}{z}=Log (z) + c\]where z is in the domain\[D=\left\{ z:z>0,\pi<\arg(z)<\pi \right\}\] and c is a complex constant. The logarithm of z is\[\log z = \ln z + i \arg (z)\]and here, specifically, \[\pi<\arg(z)<\pi\](which is the entire complex plane except for the negative real number line and 0)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Technically, you have to show that\[\frac{d}{dz}\log(z)=\frac{1}{z}\]which you can do using derivative theorems (I won't go too much more into it  may lose the point here).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0*principal* logarithm, not principle... ><

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, sort of see.....the prof told us to use integral of z dz (is complex)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hi Laurie, log(z) is complex. You can see it above when I write,\[\log(z)=\ln z + i \arg (z)\]This number is complex. You have it in the form,\[x+iy\]where\[x=\lnz\]and\[y=\arg(z)\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.