I want to find the polar form and argument of $\lvert$1+i$\rvert$
My try:
Polar form is: $re^{i\theta},$ where $r = \sqrt{2}\;$ and $\;\theta=\frac{\pi}{4}$ because $\arg(\lvert$1+i$\rvert) = \frac{\pi}{4}$
principal arg($\lvert$1+i$\rvert$) = $\frac{\pi}{4} + 2k\pi$
and the polar form is $\sqrt{2}e^{i\frac{\pi}{4}}$
Question:
is my arg, principal arg, and polar form done correctly?