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May 5th, 2012, 07:56 PM  #1 
Newbie Joined: May 2012 Posts: 1 Thanks: 0  How to deal with powers of i
While revising for my exam this week I came across a final problem in the set; Express (1+i)^i in the form a+ib I have gotten until 2^(i/2).e^(3pi/4) However what should I do from here in order to bring the i down into standard form 
May 5th, 2012, 09:53 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs  Re: How to deal with powers of i
Use the identity: and Euler's formula to get: 
May 5th, 2012, 11:36 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,974 Thanks: 1156 Math Focus: Elementary mathematics and beyond  Re: How to deal with powers of i 
May 9th, 2012, 04:53 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,974 Thanks: 1156 Math Focus: Elementary mathematics and beyond  Re: How to deal with powers of i
Here's a general solution to a complex number raised to a complex number: Computing , the angle between the complex vector and the positive real axis, in radians, using the signs of and : 

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