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December 10th, 2009, 03:51 PM  #1 
Newbie Joined: Dec 2008 From: Copenhagen, Denmark Posts: 29 Thanks: 0  Finding complex numbers that solves equation
Hi all I'm trying to find the solution for the following equation where z is a complex number. The solution should be written in the from I've accomplished this some of the way or Since the above can be written or or or But I can't figure out how to express these as Can anyone tell me how to do the last part? 
December 10th, 2009, 04:37 PM  #2 
Senior Member Joined: Dec 2009 From: Las Vegas Posts: 209 Thanks: 0  Re: Finding complex numbers that solves equation
Hi; Maybe this substitution would have been better: 
December 11th, 2009, 03:55 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717  Re: Finding complex numbers that solves equation
General approach  use polar form a + bi = r exp(iq), where r = ?(a^2 + b^2) and q=arctan(b/a), noting that q is multivalued. Use this form as an intermediate for taking square root, making sure you take into account multiplicity of the angle. After you have gotten the final results in polar, convert back to rectangle using a=rcosq and b=rsinq. 
December 13th, 2009, 06:51 AM  #4 
Newbie Joined: Dec 2008 From: Copenhagen, Denmark Posts: 29 Thanks: 0  Re: Finding complex numbers that solves equation
Thanks to both of you. Your ideas did help me understand the problem a little better, and made me look some more into my own textbooks. I actually ended up using another way to solve (I'm not sure what to call this in english, but directy translated here) "binomial equations": Using the above method to find gives me Then , , , Using the method again gives me , , Which was actually the solution given in the course material. 

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