  We present a comprehensive introduction to spacetime algebra that emphasizes
its practicality and power as a tool for the study of electromagnetism. We
carefully develop this natural (Clifford) algebra of the Minkowski spacetime
geometry, with a particular focus on its intrinsic (and often overlooked)
complex structure. Notably, the scalar imaginary that appears throughout the
electromagnetic theory properly corresponds to the unit 4-volume of spacetime
itself, and thus has physical meaning. The electric and magnetic fields are
combined into a single complex and frame-independent bivector field, which
generalizes the Riemann-Silberstein complex vector that has recently resurfaced
in studies of the single photon wavefunction. The complex structure of
spacetime also underpins the emergence of electromagnetic waves, circular
polarizations, the normal variables for canonical quantization, the distinction
between electric and magnetic charge, complex spinor representations of Lorentz
transformations, and the dual (electric-magnetic field exchange) symmetry that
produces helicity conservation in vacuum fields. This latter symmetry manifests
as an arbitrary global phase of the complex field, motivating the use of a
complex vector potential, along with an associated transverse and
gauge-invariant bivector potential, as well as complex (bivector and scalar)
Hertz potentials. Our detailed treatment aims to encourage the use of spacetime
algebra as a readily available and mature extension to existing vector calculus
and tensor methods that can greatly simplify the analysis of fundamentally
relativistic objects like the electromagnetic field.
