Just as complex numbers provide a convenient way to study oscillations, they can also be employed to model wave motion. In physics, complex numbers are commonly used in the study of electromagnetic (l...Just as complex numbers provide a convenient way to study oscillations, they can also be employed to model wave motion. In physics, complex numbers are commonly used in the study of electromagnetic (light) waves, sound waves, and other kinds of waves.
If \(\Psi=\exp [\mathrm{i}(\mathrm{kx}-\omega \mathrm{t})]\), the complex function \(\psi(x, t)\) moves round and round the unit circle in the complex plane as x and t change, as illustrated in Figure...If \(\Psi=\exp [\mathrm{i}(\mathrm{kx}-\omega \mathrm{t})]\), the complex function \(\psi(x, t)\) moves round and round the unit circle in the complex plane as x and t change, as illustrated in Figure \(\PageIndex{1}\):. This contrasts with the back and forth oscillation along the horizontal axis of the complex plane represented by \(\cos (\mathrm{kx}-\omega \mathrm{t})\).
