complex (1 Viewer)

[chousta]

ey all jst 2 questions,

The points A,B,C and D on an argand diagram represent the complex numbers 2+2i, 4, 6+2i and 4+4i respectively. Prove that ABCD is a square and find the complex number represented by the intersection of the diagonals.

"The complex number z=3-4i has to roots z1 and z2. Find z1 and z2 in the form a=ib. Show that the three points representin z, z1, z2 on the argand diagram are the vertices of a right angled triangle."(is it just me or is there stupid wording)



cheers<?xml version="1.0" encoding="UTF-16"?>

 

[jdcb4]

The points A,B,C and D on an argand diagram represent the complex numbers 2+2i, 4, 6+2i and 4+4i respectively. Prove that ABCD is a square and find the complex number represented by the intersection of the diagonals.

Just subtract B from A, C form B etc... you'll find all the moduluses.. (Modulii?) are the same Sqrt(2^2 +2^2) = 2Sqrt2
Can't thionk how to find intersection properly at moment but it'll end up being 4+2i. Should be able to add opposit corners together and didvide by two, Ie, A + C divided by two.

 

[haque]

that's insufficient(jdcb4) to prove that it's a square as like a square all the sides of a rhombus are equal and it's diagonals bisect each other. I won't provide the solution for this as these type of q u should be able to do by urself at this stage and u'll become too dependent. Have a go-try and show that the adjacent sides are perpendicular to each other and that the lengths of all the sides are the same. TYhink of vectors.

 

[pLuvia]

Chousta please stop deleting your threads, it doesn't make you any worse by asking a question in these forums, that's the whole point to a forum to ask questions/answer questions

 

[jdcb4]

Yeah, wasn't thinking, show that A-B is equal to i(A-D) or somesuch. Therefore will be a 90 degree rotation. Or as complex numbers are just ordered points you can probably use same methods as co ordinate geometry and just use rise over run to show gradients... etc. I hope you've only just started complex numbers 'cause this is really basic stuff.

 

[Slidey]

It's not about what you post. The reason we don't want you deleting them, ESPECIALLY if you or anybody else posts an answer, is because it provides some material for OTHERS to learn from as they browse.

pLuvia and I would appreciate in future if you didn't delete threads, regardless of the fact that the question has been answered (by anybody, even if it was 1 minute after you posted the thread, or if you figured it out).

Don't hesitate to post here if you are having problems with a question - we're not trying to put you off.

And finally, if somebody goes to the effort of typing up a solution, it's an insult to them to delete your thread and all their work along with it.