Proof of Cauchy Schwarz for complex numbers

[dispiriton]

Homework Statement

I am told to try and solve <x - ty, x - ty> where t = <x,y>/<y,y>
However, I am stuck at that equation and unable to manipulate it to get rid of the *

Homework Equations

The Attempt at a Solution

<x - ty, x - ty> = <x,x> - <x,ty> - <ty,x> + <ty,ty>
= mod(x)^2 + mod(y)^2 (t^2) - t*<x,y> - (<x,ty>)*

 

[Undoubtedly0]

Homework Statement

I am told to try and solve <x - ty, x - ty> where t = <x,y>/<y,y>
However, I am stuck at that equation and unable to manipulate it to get rid of the *

Greetings dispiriton! What do you mean by "the *"?

 

[micromass]

<x - ty, x - ty> = <x,x> - <x,ty> - <ty,x> + <ty,ty>
= mod(x)^2 + mod(y)^2 (t^2) - t*<x,y> - (<x,ty>)*

You could simmplify this further by working out <x,ty>*. Try to get thet out of the inproduct.

Then, make the substitution t=<x,y>/<y,y>...

 

[dispiriton]

Greetings dispiriton! What do you mean by "the *"?

Its sort of like the "bar" where it is the conjugate.