Complex numbers - describe geometrically

[jason1989]

Hi!

I was just wondering if anyone would be able to help me with a question I received recently as complex numbers homework and didn't quite understand.

There was an equation given in complex form ie. something along the lines of |z-2|=|zconjugate=2| (I cannot remember this exactly now, which I know doesn't help, but nor do I know how to convert the y=-x equation back into the given form!)

The question then stated: "describe geometrically the relation between the line and the points (2,0) and (-2,0)" There was also a dotted line drawn through the points.

Homework Statement

"Describe geometrically the realtionship between the line and the points (2,0) and (0,-2)"

Homework Equations

The Attempt at a Solution

Well, I didn't actually understand what 'desribe geometrically' meant, but it was obvious that the lines intersected at the point (1,-1) and that they were perpendicular to each other. The equation of the line passing through the two points is y=x-2, and I also found that if the line y=-x was reflected about the line x=1 the other graph was obtained.

Aside from this, though, I don't actually understand what the question is asking or how I should answer it. Any help given would be greatly appreciated.

:):):)

 

[HallsofIvy]

Hi!

I was just wondering if anyone would be able to help me with a question I received recently as complex numbers homework and didn't quite understand.

There was an equation given in complex form ie. something along the lines of |z-2|=|zconjugate=2| (I cannot remember this exactly now, which I know doesn't help, but nor do I know how to convert the y=-x equation back into the given form!)

Since you don't give the precise equation, I can't say exactly what the line should be. |z- 2| can be interpreted geometrically as the distance from z= x+ iy interpreted as the point (x,y) to (2,0). |zconjugate- 2| is the distance from (x,-y) to (2,0). Unfortunately, It is true that the distance from any point (x,y) to (2, 0) is the same as the distance from (x,-y) to (2, 0). The equation you write doesn't say anything- it is true for all points.

The question then stated: "describe geometrically the relation between the line and the points (2,0) and (-2,0)" There was also a dotted line drawn through the points.

Homework Statement

"Describe geometrically the realtionship between the line and the points (2,0) and (0,-2)"

Homework Equations

If the equation were, for example, |z-2|= |z+ 2|, that is the set of points whose distance from (2,0) is the same as the distance from (-2, 0). That, geometrically, is the perpendicular bisector of the line segment from (2, 0) to (-2, 0).

The Attempt at a Solution

Well, I didn't actually understand what 'desribe geometrically' meant, but it was obvious that the lines intersected at the point (1,-1) and that they were perpendicular to each other. The equation of the line passing through the two points is y=x-2, and I also found that if the line y=-x was reflected about the line x=1 the other graph was obtained.

Aside from this, though, I don't actually understand what the question is asking or how I should answer it. Any help given would be greatly appreciated.

:):):)

 

[jason1989]

ahhhh okay; thanks!

but I'm still not sure what I should present as a solution. Does 'describe geometrically' mean in terms of equations or words?

:D

 

[HallsofIvy]

Words. In the example I gave, the description would be "the perpendicular bisector of the line segment between (-2, 0) and (2, 0)."