EXPONENTIATION, being DEFINED, allows INVERSES. Being NONCOMMUTATIVE, these INVERSES (unlike previous cases) are distinct:

• THE LOGARITHMIC INVERSE LEADS TO REAL NUMBERS (INFINITE VECTORS OF RATIONALS).
• THE ROOT EXTRACTION INVERSE LEADS TO COMPLEX NUMBERS, FOREVER VECTORED.
  That is, making ROOT EXTRACTION TOTAL MEANS THAT THE VECTOR CAN NO LONGER BE HIDDEN. Reason:
  • NATURAL NUMBER has a single UNIT: 1.

  • INTEGERS, RATIONALS and REALS HAVE two UNITS: ⁺1, ¯1.
  • THE COMPLEX NUMBER SYSTEM HAS 4 UNITS: 1, ¯1, i, ¯i (where i = √¯1.)

  The new "imaginary" units CANNOT BE HIDDEN by mere signs (hence, "Active"). THE VECTOR FORM IS NOW UNLOOSED, to GENERATE ALL THE OTHER ARITHMETICS OF CLIFFORD NUMBERS. ARITHMETIC REDUX!

  Let's see