
Complex Analysis Complex Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 10th, 2010, 11:59 AM  #1 
Senior Member Joined: Sep 2009 Posts: 251 Thanks: 0  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? Thanks. 
November 10th, 2010, 02:15 PM  #2 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  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] 
November 10th, 2010, 03:18 PM  #3  
Senior Member Joined: Sep 2009 Posts: 251 Thanks: 0  Re: Where's the center of this circle? Quote:
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.  
November 11th, 2010, 02:59 AM  #4 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  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] 

Tags 
center, circle 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Find center of a circle  fornuftit  Algebra  2  May 23rd, 2012 11:23 PM 
inscribed circle center problem  elim  Algebra  5  January 22nd, 2011 08:36 AM 
Finding the center and radius of a circle?  thyrgle  Algebra  4  May 16th, 2010 05:10 PM 
radius and center of circle:graphing  rune2402  Algebra  4  February 27th, 2008 06:21 PM 
Segmenting a Circle; Getting the Distance from Center  luftikus143  Algebra  1  February 11th, 2008 07:26 AM 