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Complex numbers and Argan Diagram

  • #1
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 theorm)

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 wierd answer for x. Pleas etell me where I;ve gone wrong!!

Any help is greatly appreciated, thnx loads!!
 

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