Complex algebra - Dot Product

Complex Formula's - The Dot Product 1) I have to figure out how to manipulate my New Number " a " 2) The Dot Product to 3) I have to Invent " Complex Algebra " now so I can manipulate my new number : " The Time Vector " 4) I have some Idea: Multiply , add , subtract in " one form of the equation " then convert to " Units Formula " is One idea 5) I wonder if this is the " solution " to " Fermat's Theorem ", would not that be funny!! 6) Or Maybe this number is a constant and I must build a Whole number system with Reals and Complex and equate them through Basis, and Dimension Using Linear Algebra
Here are the Complex Formula's and Relationships