### Relations between two coordinate systems

Given two coordinate systems $(x,y)$ and $(x',y')$ and the relations between them
$x'=x\cos\theta+y\sin\theta$
$y'=-x\sin\theta+y\cos\theta$
Show that the norm of the vector $\vec{A}+\vec{B}$, where $\vec{A}$=(Ax ,Ay) $\vec{B}$=(Bx , By) in the $(x,y)$ coordinate system stays unchanged when moving to the $(x',y')$ coordinate system.