Solve Geometry Coordinate Homework: |Z-1|+|Z+1|=7

[nekteo]

Homework Statement

Given that Z is a complex number with condition |Z-1|+|Z+1|=7

Illustrate Z on Argand Diagram and write out the equation of Locuz Z


I attempted to figured out the equation of locus Z,
|Z-1|+|Z+1|=7
|x+yi-1|+|x+yi+1|=7
$$\sqrt{}[(x-1)^2+y^2]$$ + $$\sqrt{}[(x+1)^2 + y^2]$$ = 7
$$\sqr{}x^2 + 1 - 2x + y^2 + x^2 + 1 + 2x + y^2 = 49$$
$$\sqr{}2x^2 + 2y^2 = 47$$

it's not necessary the correct answer though...
however, I can't figure how to illustrate the diagram! help!

 

[genneth]

Assuming that your calculations are correct, that gives a circle of radius $$\sqrt{47/2}$$. However, I don't think it is... Check your algebra carefully -- squaring both sides doesn't mean get rid of square roots!

Another way to think about it is that the original equation says that the distance from a point on the locus to the points +1 and -1 add up to 7. This is the condition for an ellipse with its foci at -1 and 1! And an ellipse is only a circle if the foci coincide.

 

[Architeuthis Dux]

Hello! It seems like you are on the right track with solving the equation for the locus of Z. Your final equation, 2x^2 + 2y^2 = 47, is in the form of a circle with center at the origin and radius \sqrt{47/2}. To illustrate this on an Argand diagram, you can plot the center at (0,0) and draw a circle with the calculated radius. This represents all the possible values of Z that satisfy the given equation.

To better understand the concept of locus, think about it as a set of points that satisfy a certain condition. In this case, the condition is |Z-1|+|Z+1|=7. So all the points that lie on the circle you drew on the Argand diagram will satisfy this condition.

I hope this helps! Let me know if you have any further questions. Good luck with your homework!