My Math Forum  

Go Back   My Math Forum > College Math Forum > Complex Analysis

Complex Analysis Complex Analysis Math Forum

Thanks Tree1Thanks
  • 1 Post By mathman
LinkBack Thread Tools Display Modes
July 17th, 2015, 01:56 AM   #1
Joined: Aug 2013

Posts: 32
Thanks: 1


Hi guys, any help with this one would be great.

Z is a complex number. Sketch the locus of z that satisfied by:


I break this down to:

My thought is to select three points and place them on the imaginary axis, then deduce the coordinate of z, three times, (ie start with z on the im axis, and we can show that coordinate of z is (0,2),then place z-2 on the im axis etc)

Has anyone got an easier way to do this?

I know the answer is a circle, but how can you tell? also, My the answer shows its just a major arc of a circle, but with no explanation as to why only part of the circle exists.

if anyone can help deduce the equation and help with the above I would be appreciate it.

Thanks in advance
evaeva is offline  
July 17th, 2015, 01:41 PM   #2
Global Moderator
Joined: May 2007

Posts: 6,510
Thanks: 584

$\displaystyle \frac{z-2}{z-i}=r\frac{\sqrt{2}}{{2}}(1+i)$, where r > 0. Solve for r as a function of z and plot.
Thanks from evaeva
mathman is offline  

  My Math Forum > College Math Forum > Complex Analysis


Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Locus Monokuro Geometry 5 August 2nd, 2014 07:37 PM
Known locus? Mathmax Algebra 0 May 22nd, 2011 12:09 PM
Locus julian21 Algebra 1 November 8th, 2010 07:26 PM
LOCUS symmetry Algebra 6 January 30th, 2007 02:48 AM

Copyright © 2018 My Math Forum. All rights reserved.