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February 22nd, 2014, 11:41 AM  #1 
Senior Member Joined: Jan 2014 Posts: 196 Thanks: 3  Geometric Relationship
The question asks how to describe, geometrically, the relationship between a nonzero complex number, , and its inverse, I see that for or shrinks, and reflects each number about either axis by plugging in a few values for each. I am having a hard time coming up w/ a concise way of describing this and also wondering it there is another way of looking at this that makes this geometric relationship more obvious. Thanks for any help! 
February 22nd, 2014, 11:44 AM  #2 
Senior Member Joined: Jan 2014 Posts: 196 Thanks: 3  Re: Geometric Relationship
Ok, scratch reflects each number about either axis..... and are symmetric about the origin.

February 22nd, 2014, 01:05 PM  #3 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Geometric Relationship
Hint : use that 
February 22nd, 2014, 09:31 PM  #4 
Senior Member Joined: Jan 2014 Posts: 196 Thanks: 3  Re: Geometric Relationship
Now I have more questions, lol How do I apply the inverse function to ? ? 
February 23rd, 2014, 02:00 AM  #5 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Geometric Relationship
Let then the mapping of the point under is what ?

February 23rd, 2014, 08:22 AM  #6 
Senior Member Joined: Jan 2014 Posts: 196 Thanks: 3  Re: Geometric Relationship
I see now.... I think! 
February 23rd, 2014, 09:54 AM  #7  
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Geometric Relationship Quote:
 

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