How do I get Mathematica to Simplify this to 1?

*To*: mathgroup at smc.vnet.net*Subject*: [mg104437] How do I get Mathematica to Simplify this to 1?*From*: dushan <dushanm at spinn.net>*Date*: Sat, 31 Oct 2009 01:54:34 -0500 (EST)

After initially declaring that {w>0, k>0, {z,X,Y} el Reals}, a matrix- vector multiplication produces the vector {(X - w Cos[k z])/Sqrt[z^2 + (X - w Cos[k z])^2 + (Y - w Sin[k z])^2], (Y - w Sin[k z])/Sqrt[z^2 + (X - w Cos[k z])^2 + (Y - w Sin[k z])^2], -(z/Sqrt[ w^2 + X^2 + Y^2 + z^2 - 2 w X Cos[k z] - 2 w Y Sin[k z]])} The denominators are in fact identical. When I ask for Norm[%] I get \[Sqrt]( Abs[z/Sqrt[w^2 + X^2 + Y^2 + z^2 - 2 w X Cos[k z] - 2 w Y Sin[k z]]] ^2 + Abs[(X - w Cos[k z])/Sqrt[z^2 + (X - w Cos[k z])^2 + (Y - w Sin[k z]) ^2]]^2 + Abs[(Y - w Sin[k z])/Sqrt[z^2 + (X - w Cos[k z])^2 + (Y - w Sin[k z]) ^2]]^2 ) and Simplify[%] reproduces this identical result instead of supplying the correct answer 1. What am I doing wrong that prevents Mathematica from delivering the right answer? A separate question: Is there available somewhere a short list of symbols (such as '!!', '&&', "=.", '/@', etc.) and their meanings? A Mathematica book index would generally start with such a list, but having it available as a 1-page crib-sheet would be very helpful to newbies like me. Thanks. - Dushan