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November 26th, 2009, 04:20 PM   #1
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Very Easy Circle

Evaluate

Ok so this problem is so easy yet I got it wrong for some reason on my HW that I turned in and I want to know why. Here is what I did:







so then we have a circle centered at with radius of 2. I do not see how this is wrong but maybe I am missing something simple with the center or something. Thanks.
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November 26th, 2009, 07:08 PM   #2
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Re: Very Easy Circle

The conclusion is correct but your third step isn't particularly logical and in your fourth step you are missing the || on the left side.

In the third step it looks like you are saying that if |a| = b then |a*| = b*, where * denotes complex conjugation. This is not true.
The norm of the complex conjugate of a is the norm of a, without exception.
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November 27th, 2009, 12:16 PM   #3
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Re: Very Easy Circle

So how should I write out the third step? because I have no clue besides the way I did it.
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November 27th, 2009, 03:39 PM   #4
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Re: Very Easy Circle

"The norm of the complex conjugate of a is the norm of a , without exception."

That is, |z* + i/2| = |(z* + i/2)*| = |z - i/2| = 2

Conjugating the 2 like you did was spurious, though it didn't change the truth of the equation in step 3.
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