1. The problem statement, all variables and given/known data Let z, w be complex vectors of C^n. Prove ||w + z|| <= ||w|| + ||z|| (using the standard inner product for C^n) (i.e. <w,z> = w*z', where * is the dot product and ' denotes the complex conjugate) 3. The attempt at a solution Well, I found that ||w + z|| = sqrt( w*w' + z*z' + z*w' + w*z') = sqrt( w*w' + z*z' + <w,z> + <w,z>' ) and ||w|| + ||z|| = sqrt(w*w' + z*z') So by showing that <w,z> + <w,z>' <= 0 then I guess that will finish the proof but I am unsure of how to do this. Any help?