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Complex numbers- HELP!

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

Any help is greatly appreciated, thnx loads!!
 

Answers and Replies

319
0
Just draw a picture if your not sure and then it should be easy to see
 
I have! i've drawn the diagramme but i carn solve it and neither can my dad. I;m sorry, can u help me please? I;m doing Alvl pure maths (not further) by the way. thnx!
 
319
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so if you plot the points, b lies somewhere on x=3 and d somewhere on x=-2

and all the lines are perpendicular, so you can work out the i values of the point b and d
 
nono, but AB doesnt have to be horizontal (i.e. parallel to the x axis) the rectangle can and probably would be slanted. the condition given is AB=2CD. if AB and CD are parallel to the xaxis the condition is not satisfied
 
VietDao29
Homework Helper
1,417
1
So: you have [itex]AB = 2BC \Rightarrow AB ^ 2 = 4 BC ^ 2 [/itex]
ABC is the right triangle. You also have the length of AC. What does this suggest you?
Let [itex]b = x_B + iy_B[/itex]
So [itex]B(x_B, y_B)[/itex]
You also have [tex]\overrightarrow{BA}\overrightarrow{BC} = 0[/tex]
So you will come up with 2 equations:
[tex]\left\{ \begin{array}{l} (x_B + 2)(y_B - 3) = -(y_B + 1)(y_B - 5) \\ AB ^ 2 = (x_B + 2) ^ 2 + (y_B + 1) ^ 2 = ... \end{array} \right.[/tex]
From there you can solve for b, then d.
Viet Dao,
 
i did tht b4 i posted the qns. Tht;s where i got stuck cos the numbers were absurdly big and unfriendly, but its ok, I figured another way of doing already. thnx for ur help anyway!
 

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