Aus Online Mathematik Brückenkurs 2

We calculate what the expression will be

\displaystyle \left( 2-i \right)+\left( 5+3i \right)=2+5+\left( -1+3 \right)i=7+2i

and then take the magnitude:

\displaystyle \left| 7+2i \right|=\sqrt{7^{2}+2^{2}}=\sqrt{49+4}=\sqrt{53}

NOTE: Note that it is not possible to take the magnitude of the terms individually

\displaystyle \left| \left( 2-i \right)+\left( 5+3i \right) \right|\ne \left| 2-i \right|+\left| 5+3i \right|