geometry in complex numbers

Apr 2010
43
0
Represent the following region in the complex plane by equations or inequalities in the variable​
z.

All the points outside a circle of radius 3, centered at x=-1, y=-2.

i drew the circle -4< x < 2 and -5<y<1

so how do we do the equation or the inequality?
 

Drexel28

MHF Hall of Honor
Nov 2009
4,563
1,566
Berkeley, California
Represent the following region in the complex plane by equations or inequalities in the variable​
z.

All the points outside a circle of radius 3, centered at x=-1, y=-2.

i drew the circle -4< x < 2 and -5<y<1

so how do we do the equation or the inequality?
A circle of radius \(\displaystyle R\) around a complex number \(\displaystyle z_0\in\mathbb{C}\) is defined to be \(\displaystyle \left\{z\in\mathbb{C}:|z-z_0|=R\right\}\)
 
Apr 2010
43
0
A circle of radius \(\displaystyle R\) around a complex number \(\displaystyle z_0\in\mathbb{C}\) is defined to be \(\displaystyle \left\{z\in\mathbb{C}:|z-z_0|=R\right\}\)
i didnt understand, the equation of a circle is |z-z_0|=R but how do we do the above as an inequality or equation?
 

Plato

MHF Helper
Aug 2006
22,462
8,634
\(\displaystyle \left\{ {z:\left| {z - \left( { - 1 - 2i} \right)} \right| > 3} \right\}\).
 
Apr 2010
43
0
\(\displaystyle \left\{ {z:\left| {z - \left( { - 1 - 2i} \right)} \right| > 3} \right\}\).
oh ok thankyou very much now i understood what they want and how to solve questions like that. thanks again