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.