complex numbers (1 Viewer)

[NizDiz]

Hey guys, how do i prove this;

z * conjugate z = x^2 + y^2 = |z|^2

All help gr8ly appreciated. Thanks!!

 

[Carrotsticks]

Let z=x+iy.

 

[NizDiz]

what does |z|^2 equal to, and how do u work that out?

 

[kev-kun]

Remember to note that
<img src="http://latex.codecogs.com/gif.latex?|z|=\sqrt{x^2&plus;y^2}&space;\\&space;So&space;|z|^2=x^2&plus;y^2&space;\\&space;\therefore=(x&plus;iy)(x-iy)" title="|z|=\sqrt{x^2+y^2} \\ So |z|^2=x^2+y^2 \\ \therefore=(x+iy)(x-iy)" />

 

[braintic]

what does |z|^2 equal to, and how do u work that out?

So you don't know how |z| is related to x and y through Pythagoras theorem?

 

[NizDiz]

thanks for the help!! gr8ly appreciated