Solution
= Solution
The <complex exponential> factors as $e^{(3+i)(a+ib)}=e^{3a-b}e^{i(a+3b)}$. Its positive real prefactor is its <modulus>, while its phase gives its <complex argument>:
$$
\boxed{|e^{(3+i)z}|=e^{3a-b},\qquad\arg(e^{(3+i)z})=a+3b\pmod{2\pi}.}
$$
For the principal <complex argument>, reduce $a+3b$ to the chosen principal interval.