Help with school homework (1 Viewer)

[RachelGreen]

Can anyone help me with this complex question please?
The complex numbers z = x+iy and w=u+iv are such that w = z+2/z.
(a) Express w in the form of u +iv
(b) Hence, find and describe the locus of w if z moves along the unit circle.

I did (a) already and is stuck on (b). Answer I got for (a) is w = (x^2+2x+y^2) / (x^2 + y^2) - i(2y/x^2 + y^2)

Thanks in advance!

 

[Drsoccerball]

Can anyone help me with this complex question please?
The complex numbers z = x+iy and w=u+iv are such that w = z+2/z.
(a) Express w in the form of u +iv
(b) Hence, find and describe the locus of w if z moves along the unit circle.

I did (a) already and is stuck on (b). Answer I got for (a) is w = (x^2+2x+y^2) / (x^2 + y^2) - i(2y/x^2 + y^2)

Thanks in advance!

The key to this question is what I have made bold. This statement means that :

 

[Ekman]

The key to this question is what I have made bold. This statement means that :

Actually no.

 

[Drsoccerball]

Actually no.

 

[Ekman]

I was just correcting your statement about just so there was no confusion.

In terms of this question, it doesn't matter, since the square root of 1 is still 1, however for cases where the radius is not 1, then you would have got it wrong.

 

[RachelGreen]

I still don't get how to do it ??/?

 

[dan964]

I still don't get how to do it ??/?

it is given that z lies on the unit circle which is
hence for all values of z (and hence w); that expression is true.

(Hint: hence substitute it in. Attempt the problem first, I won't give the answer)

Then once you have simplified it down, you should be able to plot in on an Argand diagram; (or if you are smart you don't need to graph) and should be able to see what type of shape of the locus is; and therefore can describe it.

(side note: |z|=1 is equivalent as )

 

[RachelGreen]

OK I GOT IT, thank you guys!