$\displaystyle |e^{iwt}|$ = 1

I've seen this expression a few times but without an explanation. Is the following true:

$\displaystyle z = re^{iwt} = r(cos(wt) + isin(wt))$

$\displaystyle |z| = ( cos(wt)^{2} + sin(wt)^{2} )^{1/2} = (1)^{1/2} = 1$

I don't have the $\displaystyle i$ included inside the square root though... Is that by convention? Because we're talking about something that's supposed to have a real value?

Thanks for your help. (Bow)