A derivation of precessional effects in the Foucault pendulum using complex numbers

It is found that the exact equations governing the motion of the Foucault pendulum take a simpler form when describing the pendulum's position as a complex number evolving in the complex plane. In this description, three notable effects (the intrinsic precession, the Foucault precession, and the Crane effect) appear as natural solutions without prior assumptions on their precessional nature. The pedagogical value of the problem is discussed, emphasizing its connections to time-reversal symmetry and the use of complex numbers in two-dimensional problems.