Let z = 4e^i(pi/6)
find iz and |e^iz|
what is iz?
is it imaginary part of z?
I would assume so. Can you do that part?
For the second part note that
$\displaystyle \left|z\right|=\sqrt{\Re^2(z)+\Im^2(z)}$ and since $\displaystyle \Re\left(e^{iz}\right)=\cos(z),\Im\left(e^{iz}\rig ht)=\sin(z)$ it follows that $\displaystyle \left|e^{iz}\right|=\sqrt{\sin^2(z)+\cos^2(z)}=1$. Another way to realize this is that $\displaystyle e^{iz}$ is some point $\displaystyle \zeta$ on the unit circle. Thus $\displaystyle \left|e^{iz}\right|$ is the length of the radius $\displaystyle \overline{O\zeta}$, but since this is the unit circle this is trivially one.