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May 21st, 2013, 02:19 AM  #1 
Newbie Joined: May 2013 Posts: 10 Thanks: 0 
Hi I need to find the angle between two vectors which are represented by complex numbers using a program. I should not convert these in to polar for because it costs me processor cycles. So, how can I find the angle difference between two complex numbers? Thanks and Regards Last edited by skipjack; April 16th, 2015 at 06:02 PM. 
May 21st, 2013, 02:24 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,163 Thanks: 472 Math Focus: Calculus/ODEs  Re: How to find the difference between angles of two complex
I would use: 
May 21st, 2013, 03:51 AM  #3 
Newbie Joined: May 2013 Posts: 10 Thanks: 0  Re: How to find the difference between angles of two complex
Hi Mark, thanks for reply. Actually I need a method which has less complexity to implement. In this method I need to calculate tan1 two times which burdens my hardware. Is there any less complex method? Regards Ashok 
May 21st, 2013, 11:28 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,054 Thanks: 1618  
May 21st, 2013, 12:31 PM  #5 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: How to find the difference between angles of two complex
You can use the dot product, just pretend the numbers are real. In the complex plane, the complex vector <a, bi> corresponds to the real vector <a, b> in the cartesian real plane. It uses arccos instead of arctan but i doubt this method is simpler than the others offered. 
May 21st, 2013, 08:29 PM  #6  
Newbie Joined: May 2013 Posts: 10 Thanks: 0  Re: How to find the difference between angles of two complex
Hi Thanks for the reply. But I think it won't give negative angles... Actually I need negative angles too. Is there any method for that? Regards Quote:
 
May 21st, 2013, 10:43 PM  #7  
Newbie Joined: May 2013 Posts: 10 Thanks: 0  Re:
Dear Friend, Thanks for the solution, it has taken me to better position. But it is still not meeting my time constraint Actually I have one more step after this, shifting the phase of second vector based on the angle difference What is the method to do these steps together ? (with least complexity , so best timing efficiency) Regards Quote:
 
May 21st, 2013, 11:54 PM  #8 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: How to find the difference between angles of two complex
You are correct of course, I forgot the usual range of arccos, so absolute value not necessary. 
May 22nd, 2013, 12:31 AM  #9  
Newbie Joined: May 2013 Posts: 10 Thanks: 0  Re: How to find the difference between angles of two complex
Without absolute the answer it's getting add complex number. I did like this in Matlab acos((dot(v1,v2))/(abs(v1)*abs(v2))) please check if it is correct Quote:
 
May 22nd, 2013, 06:57 AM  #10  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: How to find the difference between angles of two complex Quote:
I would test the code using A = <3, 4> B = <6.6, 11.2> If it gives 67.38° as an answer then it's most likely correct. I got those 2 vectors by putting a 5,12,13 triangle on the hypotenuse of a 3,4,5 triangle with its base 3 on the x axis, you can tell that by looking at vector A. Notice the components of B are 'nice' and not some ghastly irrationals. The test is not a proof that the code works, but I think the vectors A, B are sufficiently diverse to avoid any nasty coincidences for this problem. If you don't get 67.38° then this proves the code doesn't work.  

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angles, complex, difference, find, num 
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