Complex Numbers - Q (1 Viewer)

[Mathematician]

Given w=u+iv , u = x - x/(x^2+y^2) ,v = y + y/(x^2+y^2)

and that x^2 + y^2=1

Find the locus of w


PLZ RESPOND QUICKLY!!! haha


Thanks

 

[turtle_2468]

Hmm. Doesn't that simplify to u=x-x=0
and v=y-y=0?
Which means w=0...
Because x^2+y^2=1
or maybe you're drunk... (the last haha was disturbing..)

PS Truemathematician is a subgroup of Truephysicists, not the other way round!

 

[wogboy]

u = x - x/(x^2 + y^2)
v = y + y/(x^2 + y^2)

also x^2 + y^2 = 1,

so u = x - x = 0
v = y + y = 2y

so w= 2iy, where -1<=y<=1 (this is because y must be between 1 and -1, to keep x real, in the relation x^2 + y^2 = 1)

or w = ti where -2<=t<=2

Geometrically this represents a line (of length 4 units) going from (0,-2) to (0,2) (along the y-axis), in an Argand diagram.

 

[Mathematician]

..

HAHA IM NOT DRUNK


I knew the answer for the locus was x=0 but we exclude the origin (0,0) why??????????????????

And thanx wogboy, the book didnt include it goes from (0,-2) to (0,2) haha- they missed something, and u missed we exclude the origin.

 

[wogboy]

umm I don't see why we have to exclude the origin.

let x = 1, y = 0.
then x^2 + y^2 = 1 is satisfied,
therefore u = 1 - 1/1 = 0 (as per normal)
and v = 0 - 0/1 = 0
so w = 0 + 0i = 0
therefore the origin should be a valid pt.

 

[Mathematician]

...

I dont know, maybe i should add
w= z-1/z ( given) which is what yielded the expressions for u and v in terms of x and y.[so really u should be able to work backwards to see that for urself, right?)

if z=0 w is undefined?????



Is that right???


"PS Truemathematician is a subgroup of Truephysicists, not the other way round!"


Im saying u have to be a good mathematician to be a good physicist. Well i guess fardaday wasnt educated math, and he was good so there are SOME exceptions. Your saying u must be a good physicist to be a good mathematician????

NOPE. Mathematics tends to illude people into a different perspective, away from the physical worlds perspective of whats going on. Even the best of mathematicians.People even tend to forget that there are forces on an object undergoing a certain motion and that these forces are what governs the motion of the object and shape of the trajectory and not the equations that describe it.
BIG ILLUSION.

 

[wogboy]

What is the value of z? Can you post the full question, because I can't tell whether it's right or not without further info.

 

[Mathematician]

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