$$ \xi_{\pm} = ip\sin(w) \pm i\sqrt{p^2\sin^2 w-1}$$
if i take the modulus of this complex number what will I get?
is it
$$ ( ip\sin w \pm i\sqrt{p^2 \sin^2 w-1}) ( -ip\sin w\pm -i\sqrt{p^2\sin^2 w-1}) \text{ ?}$$
and also can someone show me the modulus of this number
$$ ip\sin w \pm i\sqrt{1-p^2\sin^2 w}$$
the answer is $1,$ but not sure how to get this cause of the plus and minus sign.
Hint. If $x\in \Bbb R$ then $|ix|=|x|$.