conditional explanation formed type

given:

interface i
{
}

class b: i
{
}

class c: i
{
}

class a
{

    open vacant method(b arg)
    {
    }

    open vacant method(c arg)
    {
    }

    open vacant method(i arg)
    {
       // slight i wish simplify.
       (i b)
       {
          this.method(arg b);
       }
       else (i c)
       {
          this.method(arg c);
       }
    }
}

i know there improved ways settlement form interactions, nonetheless since
details take too enlarged explain possible.
since settlement repetitious times, i reinstate the
conditional explanation general doing i only line.
i can't rudimentary proceed exercise general method/class, nonetheless instincts tell me should possible.

any assistance appreciated.