Complex numbers assistance (1 Viewer)

[epsilon-]

How can I do this?

|a|^2 + |b|^2 - |a-b|^2 = 2Re(a bconjugate)

Thanks.

 

[Sy123]

if we let





It becomes clear that,

 

[anomalousdecay]

Let: a=x + iy, b= x - iy
|a|^2 = x^2 + y^2
|b|^2 = x^2 + y^2
a-b = 2yi
|a-b| = sqrt(4y^2) = 2y

2x^2 + 2y^2 + 2y = 2Re(x^2 - y^2) = x^2 -y^2
3y^2 + x^2 + 2y = 0

The locus of a is: 3y^2 + x^2 + 2y = 0, which represents an ellipse.

 

[anomalousdecay]

Hang on. Does the question ask to prove it or to find the locus defined as that?

 

[epsilon-]

if we let





It becomes clear that,

Fanks MOIT! <3

Let: a=x + iy, b= x - iy
|a|^2 = x^2 + y^2
|b|^2 = x^2 + y^2
a-b = 2yi
|a-b| = sqrt(4y^2) = 2y

2x^2 + 2y^2 + 2y = 2Re(x^2 - y^2) = x^2 -y^2
3y^2 + x^2 + 2y = 0

The locus of a is: 3y^2 + x^2 + 2y = 0, which represents an ellipse.

Fanks MAiTE! <3

Hang on. Does the question ask to prove it or to find the locus defined as that?

No

 

[anomalousdecay]

So are we both correct in that sense? Wow I have never come across general questions like that before.