Solution
= Solution
Write $1+i=\sqrt2e^{i\pi/4}$ and multiply the phases:
$$
z=\sqrt2e^{i(\pi/4+\pi/6)}=\sqrt2e^{5\pi i/12}.
$$
Therefore
$$
\boxed{|z|=\sqrt2,\qquad\arg z=\frac{5\pi}{12}+2\pi k,\quad k\in\mathbb Z.}
$$
The displayed representative already lies in the principal argument <interval>.