Look up Quantity
in the documentation:
Quantity[314.159, "Meters"] *
Sqrt[Quantity[7.34102*10^-6 - 0.0000178801 I,
"Seconds"^2/"Meters"^2] ]/Quantity[1, "Seconds"]
% // Coth
You can also use your notation, but adding the information that s
and m
are positive:
(314.159 m *
Sqrt[((7.34102*10^-6 - 0.0000178801 I)
s^2)/m^2])/s
Simplify[%, s > 0 && m > 0]