  Closed form expressions in a coordinate-free form in real Clifford geometric
algebras (GAs) Cl(0,3), Cl(3,0)$, Cl(1,2) and Cl(2,1) are found for exponential
function when the exponent is the most general multivector (MV). The main
difficulty in solving the problem is connected with an entanglement or mixing
of vector and bivector components. After disentanglement, the obtained formulas
simplify to the well-known Moivre-type trigonometric/hyperbolic function for
vector or bivector exponentials. The presented formulas may find wide
application in solving GA differential equations, in signal processing,
automatic control and robotics.
