Complex numbers and Argan Diagram

[coffeebeans]

Hi,
I desperately need help with this qns:
In an Argan Diagram, the points A, B, C, D represent the copmlex numbers a,b,c,d respectively. Guiven that ABCD is a rectangle describd in an anticlocwise sense, with AB=2CB, and a=-2-i, c=3+5i, find b and d
(AB and CD are not parallel to the xaxis)

I've tried using dot product and gradient method, by letting B be (x,y), it all comes down to the equation y^2-4y-5+x^2-6-x=0 ---- (1)

|AC| = sqrt 61, and since ABC makes a right angled triangle, CB=1 unit, AB=2 units, therefore AB=sqrt 61 divided by sqrt5 multipled by 2 (pythagoras theorem)

Then i equate that sqrt61/sqrt5 x 2 to the magnitude of AB(i.e. sqrt((x+2)^2 + (y+1)^2) and equated this equation to equation 1 by elimination.

After which i ended up with a weird answer for x. Pleas etell me where I;ve gone wrong!

Any help is greatly appreciated, thnx loads!

 

[Doc Al]

Please do not double post! https://www.physicsforums.com/showthread.php?t=86398

 

[thepatientmental]

Hi there,

It looks like you're on the right track with using the Pythagorean theorem to find the length of AB. However, there are a few things that may have gone wrong in your calculations.

Firstly, when you equate the magnitude of AB to the equation you have for AB in terms of x and y, you should not be using the Pythagorean theorem again. Instead, you should be using the fact that AB=2CB, which means that the magnitude of AB is twice the magnitude of CB.

Secondly, when you equate the magnitude of AB to the equation in terms of x and y, you should not be equating it to equation (1). Instead, you should be equating it to the equation for the magnitude of AB, which is sqrt((x+2)^2 + (y+1)^2). This will give you a different equation to work with.

Once you have the correct equation, you can solve for x and then substitute it into the equation for the magnitude of AB to solve for y. This will give you the coordinates of B, and from there you can use the same method to find the coordinates of D.

I hope this helps! Just remember to always check your equations and make sure you are using the correct equations for the given information. Good luck!