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November 10th, 2010, 10:59 AM   #1
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Where's the center of this circle?

Stupid question here (I assume):

C: |z+1/4|=1/2
is a circle of radius 1/2 centered at 1/2 on the complex plane. Right? Why is someone saying it's centered at -1/2 on the plane.

If z=0, z+/4 is 1/4. Then the radius should stretch 1/2 in all directions from there. Right?
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November 10th, 2010, 01:15 PM   #2
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Re: Where's the center of this circle?

[color=#000000]The circle of center and radius on the complex plain is . So for your example , which means that the circle is centered at and has radius .[/color]
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November 10th, 2010, 02:18 PM   #3
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Re: Where's the center of this circle?

Quote:
Originally Posted by ZardoZ
[color=#000000]The circle of center and radius on the complex plain is . So for your example , which means that the circle is centered at and has radius .[/color]
OK, I can follow that easy enough. But what I guess I'm really asking is "why"? Why is the center at (-1/4,0) (or why is it at -z_0 in the general equation)?

Isn't the center going to be when z=0? And when z=0 for the circle |z+1/4|=1/2, the point is (0,1/4). So the center should be (0,1/4), and z will circle (0,1/4) at a distance of |1/2|? Put another way, the magnitude of z from 1/4 will always be 1/2. 1/2 unit away the point 1/4. Either the theorem you quote is wrong (it's not!) or my thought process is wrong. But I can't see what's wrong with my thinking for the life of me.
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November 11th, 2010, 01:59 AM   #4
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Re: Where's the center of this circle?

[color=#000000]When you have an equation which represents a circle on the complex plain, this means that you are talking about the points that are on the circle, not inside the circle. Above you took which means that it is an internal point of the circle not a boundary one which is the correct. What you say though could be right , if which represents the points that are interior points plus the boundary ones.[/color]
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