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February 22nd, 2014, 11:41 AM   #1
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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!
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February 22nd, 2014, 11:44 AM   #2
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Re: Geometric Relationship

Ok, scratch reflects each number about either axis..... and are symmetric about the origin.
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February 22nd, 2014, 01:05 PM   #3
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Re: Geometric Relationship

Hint : use that

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February 22nd, 2014, 09:31 PM   #4
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Re: Geometric Relationship

Now I have more questions, lol

How do I apply the inverse function to ?

?
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February 23rd, 2014, 02:00 AM   #5
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Re: Geometric Relationship

Let then the mapping of the point under is what ?
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February 23rd, 2014, 08:22 AM   #6
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Re: Geometric Relationship

I see now.... I think!

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February 23rd, 2014, 09:54 AM   #7
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Re: Geometric Relationship

Quote:
Originally Posted by WWRtelescoping
I see now.... I think!

Correct , can you see know what happen to the modulus and the argument ?
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