Represent graphically the set of values of z for which |z+3|=|z-2i|

Answer 1

using complex domain plane z=x+iy, which in polar form (z=|z|*e^iθ )

has magnitude of |z|= √[x²+y²]

question is when is magnitude of z+3 equal magnitude of z-2i

same as when

(x+3)²+y²=x²+(y-2)²

^....

y=-(3/2)x-5/4

problem asks the line be drawn on z plane

on z plane, all x,y points on that line will solve equation



check, x=0, y=-5/4

z-2i=-0-(13/4)i, magnitude 13/4

z+3=3-(5/4)i magnitude 13/4

Answer 2

| z + 2i | = √5

| z + 3 | = √5

z + 3 = ±√5