# complex numbers problem

• December 14th 2008, 09:58 AM
Haris
complex numbers problem
http://img522.imageshack.us/img522/773/complex3xr8.png
How would you go about showing this?
• December 14th 2008, 10:12 AM
Plato
Just multiply and collect terms: $\left[ {\left( {a + bi} \right)+\left( {c + di} \right)} \right]\left[ {\left( {a - bi} \right)+\left( {c - di} \right)} \right]$
• December 14th 2008, 10:14 AM
Moo
Hello,
Quote:

Originally Posted by Haris
http://img522.imageshack.us/img522/773/complex3xr8.png
How would you go about showing this?

You can do it in two ways.

1st :
Write z and w with their real and imaginary parts and expand the LHS

2nd :
Use these rules :
$z\bar z=|z|^2$ for any complex number
$z+\bar z=2 \ \Re(z)$
$\bar z+\bar w=\overline{z+w}$
and then expand the LHS

There is another rule, but you don't need it here :
$z-\bar z=2 \ \Im(z)$