Basic question: is the std of complex numbers the std of its components?

Sorry for the basic question, I searched the internet but could not get a simple and clear answer.

I want to compute the std of a direction / bearing , values are from 0-360.
I can convert the values into complex numbers and back to have a proper average.

Can I convert my angles into complex numbers, compute the std of the real and imag parts and convert the result back to degrees and have the correct std of my angles?

Am I missing something?

Thank you so much for you help, it is very appreciated!!!


Less is more. Stay pure. Stay poor.
Not my area at ALL, but this seems feasible to me. This is not based on any source, etc. - just intuition. Do others report angle degrees with std? Have you seen them reported this way?