S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Tue, 21 May 2013 10:39:41 UTC

All times are UTC [ DST ]




Post new topic Reply to topic  [ 6 posts ] 
Author Message
 Post subject: Complex exponential equation
PostPosted: Tue, 14 Sep 2010 17:28:06 UTC 
Offline
Math Cadet

Joined: Fri, 18 Dec 2009 14:15:51 UTC
Posts: 6
Heya

I cant get my head around this one:

e^z = 1 , where z is a complex number

.. what is z ?

thanks


Top
 Profile  
 
 Post subject:
PostPosted: Tue, 14 Sep 2010 18:36:53 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3690
Location: Ottawa Ontario
HINT: (anything)^0 = 1

_________________
I'm not prejudiced...I hate everybody equally!


Top
 Profile  
 
 Post subject: Re: Complex exponential equation
PostPosted: Tue, 14 Sep 2010 19:48:07 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame
User avatar

Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9632
rkj66 wrote:
e^z = 1 , where z is a complex number

.. what is z ?

z=a+ib

e^z=e^{a+ib}=e^a(\cos b+i\sin b)=1

In order for this to work, we must have a = 0 and b=2\pi n


Top
 Profile  
 
 Post subject: Re: Complex exponential equation
PostPosted: Wed, 15 Sep 2010 21:09:54 UTC 
Offline
Math Cadet

Joined: Fri, 18 Dec 2009 14:15:51 UTC
Posts: 6
Matt wrote:
rkj66 wrote:
e^z = 1 , where z is a complex number

.. what is z ?

z=a+ib

e^z=e^{a+ib}=e^a(\cos b+i\sin b)=1

In order for this to work, we must have a = 0 and b=2\pi n


Thanks for the tip .. that helped. Now i wonder if there is a general solution for the equation:

e^z = c

??


Top
 Profile  
 
 Post subject:
PostPosted: Thu, 16 Sep 2010 01:13:02 UTC 
Online
Moderator
User avatar

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
Denis wrote:
HINT: (anything)^0 = 1


Remember that complex numbers work differently, so 0 isn't the only thing...

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination


Top
 Profile  
 
 Post subject: Re: Complex exponential equation
PostPosted: Thu, 16 Sep 2010 08:35:16 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame
User avatar

Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9632
rkj66 wrote:
Now i wonder if there is a general solution for the equation:

e^z = c

Read about the complex logarithm. If you're taking a complex analysis course, then you'll learn about it eventually.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 6 posts ] 

All times are UTC [ DST ]


Who is online

Users browsing this forum: No registered users


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2011 phpBB Group.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA