October 1st, 2016, 07:57 AM  #1 
Newbie Joined: Oct 2016 From: Lawrence, Kansas Posts: 2 Thanks: 0  graphing set
How do I graph a set that is defined as z given that z [complex number] <= 1 (apologies: I am approaching an online class with an undeniably weak background, but with determination....). Last edited by skipjack; October 22nd, 2016 at 10:31 AM. 
October 1st, 2016, 08:06 AM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,105 Thanks: 576 
You'll see the expression $z  z_0$ a lot. The region $zz_0 \leq \rho$ is a disk on the complex plane of radius $\rho$, centered at the point $z_0$. Last edited by skipjack; October 22nd, 2016 at 10:32 AM. 
October 1st, 2016, 08:27 AM  #3 
Newbie Joined: Oct 2016 From: Lawrence, Kansas Posts: 2 Thanks: 0 
Thanks!
Last edited by skipjack; October 22nd, 2016 at 10:31 AM. 
October 22nd, 2016, 09:38 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,342 Thanks: 588 
Specifically, in the "complex" plane z= x+ iy. Writing point $\displaystyle z_0$ as a+ iy, then $\displaystyle z z_0= x+ iy (a+ ib)= (x a)+ i(y b)= \sqrt{(xa)^2+ (y b)^2}$ so that $\displaystyle z z_0\le \rho$ is $\displaystyle \sqrt{(x a)^2+ (y b)^2}\le \rho$ and squaring both sides, $\displaystyle (x a)^2+ (y b)^2\le \rho^2$. $\displaystyle (x a)^2+ (y b)^2= \rho^2$ is the circle, in the complex plane with center $\displaystyle z_0= a+ ib$ and radius $\displaystyle \rho$. 

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