How would you go about showing this?
Hello,
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 :
$\displaystyle z\bar z=|z|^2$ for any complex number
$\displaystyle z+\bar z=2 \ \Re(z)$
$\displaystyle \bar z+\bar w=\overline{z+w}$
and then expand the LHS
There is another rule, but you don't need it here :
$\displaystyle z-\bar z=2 \ \Im(z)$