CAS : best way to display normalized complexes ?

[primer]

Hello,
I have complex numbers and I'm searching for the best way to display it, in normalized algegraic form : a + i*b.
with this rule : no sqr on denominator 1/sqr(2) -> sqr(2)/2


Let's start with a very simple example
I have this complex : 1/sqr(2) - i* 1/sqr(2)
and I want to display sqr(2)/2 -i*sqr(2)/2
I tried simplify(), normal(), collect() : no success.

another example : (x+i*y)/(x+i*y-i)
I would like to manipulate this by multiplying nominator and denominator with conjugate... in order to have only reals at denominator.
is there such a rewite function for that ?

Thank you.

[parisse]

Try with sqrt and evalc.