
Complex Analysis Complex Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 28th, 2012, 11:02 AM  #1 
Member Joined: Oct 2012 Posts: 36 Thanks: 0  complex number calculation
Evaluate {(1+i)^(1i)} and describe the set{1^x} when x is a real number, distinguish between the cases when x is rational and when x is rational. for now considering the complex number. i dont know how to start with,for firest part i just write it into e^((1i)log(1+i)) then get the number with e to the power which inculding i , and the secound part , for 1=e^(i2npi) then 1^x is e^(2inxpi) then how to consider the case for rational and irrational here?????

November 28th, 2012, 02:28 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,524 Thanks: 588  Re: complex number calculation
When x is rational there are only a finite number of solutions, while for x irrational there are an infinite number of solutions.

November 28th, 2012, 02:44 PM  #3  
Member Joined: Oct 2012 Posts: 36 Thanks: 0  Re: complex number calculation Quote:
 
November 29th, 2012, 12:41 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,524 Thanks: 588  Re: complex number calculation
Every value of n gives a different angle. Proof by contradiction: Assume two values (n and m) give the same angle, then xm  xn would be an integer k, so x = k/(nm) which is rational. 

Tags 
calculation, complex, number 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Complex coordinate bearing calculation problem, need help…  TheSwede  Algebra  0  January 10th, 2014 11:05 AM 
Complex Number!  tkttan  Algebra  2  September 19th, 2013 04:31 AM 
complex number  Number Theory  3  January 20th, 2011 05:15 AM  
Finding real number in complex number  TsAmE  Complex Analysis  1  October 18th, 2010 04:38 PM 
Complex probability calculation  toltec7  Advanced Statistics  1  May 14th, 2008 07:30 PM 