Btw, there are a number of ways to write that expression depending on the complexity of the function

Short syntax:

   Enum.map [1,2,3], &(&1 * &1)

Long syntax:

   Enum.map [1,2,3], (fn num ->
     num * num
   end)

Or even:

   square_me = &(&1 * &1)
   Enum.map [1,2,3], square_me

   square_me_too = fn(num) -> num * num end
   Enum.map [1,2,3], square_me_too

Defining a function separately (e.g. even in another module) and referencing it:

   def square(num) do
      num * num
   end

   def doing_something() do
      ...

      Enum.map [1,2,3], &square/1
      Enum.map [1,2,3], &SomeOtherModule.square/1

      ...
   end

yeah and in Ruby, you can do:

    class Array
      def square
        map {|e| e * e}
      end
    end

Why storing code in a seperate module is a superior way than storing code in its class?

You've now altered a global object which other code may rely on. Indeed, you may overwrite someone else's Array#square method (or have yours overwritten). As a separate module, the additional code is logically distinct. You can find many discussions about monkey-patching elsewhere. It's not my intent here to argue one way or the other, just to answer your question as to why one may choose package the code as a separate module.

If it is to be reused by other modules, or if it is complex (and likely itself needs to be split up into smaller functions)

Think of:

   items = ["file_a", "file_b", "file_c"]
   Enum.map items, &HelpfulDownloaderModule.download/1

download/1 is probably pretty complex and/or can be of use in other pieces of code.

Ive been studying functional languages for the most part of 2017 and the first example makes more sense to me.