Prove that every non-zero translation Tb is a composition of two reflections in lines which are perpendicular to the direction of vector b. Note: Tb(z) = z+b where z,b[tex]\in[/tex]C My guess at how to start this is to assume b = rei[tex]\theta[/tex] where r = |b| and [tex]\theta[/tex]=arg b, so then the direction of b is b/|b| = ei[tex]\theta[/tex]. Therefore the unit vector with the direction orthogonal to b would be c = ei([tex]\theta[/tex] + [tex]\pi[/tex]/2). From there, I am shaky about what to do. I attempted to create two reflection f,g that reflection over lines with the same direction as c and I attempted to do g[tex]\circ[/tex]f and I should end up with Tb but my work gets more and more complicated. Thanks for your help.