My Math Forum complex number calculation

 Complex Analysis Complex Analysis Math Forum

 November 28th, 2012, 12:02 PM #1 Member   Joined: Oct 2012 Posts: 36 Thanks: 0 complex number calculation Evaluate {(1+i)^(1-i)} 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^((1-i)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, 03:28 PM #2 Global Moderator   Joined: May 2007 Posts: 6,684 Thanks: 659 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, 03:44 PM   #3
Member

Joined: Oct 2012

Posts: 36
Thanks: 0

Re: complex number calculation

Quote:
 Originally Posted by mathman When x is rational there are only a finite number of solutions, while for x irrational there are an infinite number of solutions.
when x is rational then it is p/q then thats the q roots of 1,but hows the idea for irrational. can u explain it with more details???? should it just consider that 1^x=exp(2ikpix) then x is irrational and i is infinite many values that i can chooes????

 November 29th, 2012, 01:41 PM #4 Global Moderator   Joined: May 2007 Posts: 6,684 Thanks: 659 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/(n-m) which is rational.

 Tags calculation, complex, number

,

,

,

prove log 1 =i2npie

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post TheSwede Algebra 0 January 10th, 2014 12:05 PM tkttan Algebra 2 September 19th, 2013 05:31 AM Number Theory 3 January 20th, 2011 06:15 AM TsAmE Complex Analysis 1 October 18th, 2010 05:38 PM toltec7 Advanced Statistics 1 May 14th, 2008 08:30 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top