Argand Diagram - Complex numbers

Mar 2015
20
0
Auckland
How would you show the sets of points for which

|z - 3 - 4i| is less than or equal to 5
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
|a- b| is the distance from complex numbers a and b so |z- (3+ 4i)| is the distance from 3+ 4i to the point z. The set of all points, z, so that the distance to 3+ 4i is 5 is a circle with center 3+ 4i and radius 5.
 
Mar 2015
20
0
Auckland
|a- b| is the distance from complex numbers a and b so |z- (3+ 4i)| is the distance from 3+ 4i to the point z. The set of all points, z, so that the distance to 3+ 4i is 5 is a circle with center 3+ 4i and radius 5.
I think I understand up to that part but in the shown working of
this question, it suddenly has |z - (3+4i)|<|z - (-1 + 2i)|
 

Plato

MHF Helper
Aug 2006
22,490
8,653
How would you show the sets of points for which |z - 3 - 4i| is less than or equal to 5
To plot this draw a closed disk in the plane with centre $3+4\bf{i}$ and radius $5$.