Given two points z1 and z2 in C, draw the picture of the set

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warwick

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Given two points z1 and z2 in C, draw the picture of the set

A = {z | |z - z1| = |z - z2|}.

I know that this is an easy problem; I just want to make sure that I'm interpreting it correctly. This is the set of all z in the complex plane such that each element is simultaneously equidistant from z1 and z2.

I can draw a line connecting z1 and z2 and then a perpendicular line to the initial line which would be the set A.
 
warwick said:
Given two points z1 and z2 in C, draw the picture of the set

A = {z | |z - z1| = |z - z2|}.

I know that this is an easy problem; I just want to make sure that I'm interpreting it correctly. This is the set of all z in the complex plane such that each element is simultaneously equidistant from z1 and z2.

I can draw a line connecting z1 and z2 and then a perpendicular line to the initial line which would be the set A.
Click to expand...
Yes, with one slight correction which I think you meant but didn't say: 'a line connecting z1 and z2 and then a perpendicular line to the initial line, intersecting at the midpoint between z1 and z2, which would be the set A.
 
Ishuda said:
Yes, with one slight correction which I think you meant but didn't say: 'a line connecting z1 and z2 and then a perpendicular line to the initial line, intersecting at the midpoint between z1 and z2, which would be the set A.
Click to expand...

Yes, sorry for the impreciseness. Thanks for the correction.
 
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