Processing math: 28%
Google
 
Web unafbapune.blogspot.com

Friday, November 15, 2013

 

|z3|=1

What does |z3|=1 look like ? A circle of radius 1, centered at 3.

What does |1z3|=1 look like ?
  |1z3|=1|13zz|2=1|13z|2=|z|2(13z)¯(13z)=z¯z(13z)(13¯z)=z¯z13z3¯z+9z¯z=z¯z8z¯z3z3¯z+1=0z¯z38z38¯z+18=0(z38)(¯z38)3282+18=0|z38|2=164|z38|=18
A circle of radius \displaystyle \frac{1}{8}, centered at \displaystyle \frac{3}{8}.

More at Analysis of a Complex Kind.


Comments: Post a Comment

<< Home

This page is powered by Blogger. Isn't yours?