Influid dynamics, complex functions are used to describe potential flow in two dimensions. Fractals.
Certain fractals are plotted in the complex plane, e.g. the Mandelbrot set
Fluid Dynamics and its sub disciplines aerodynamics, hydrodynamics,
and hydraulics have a wide range of applications. For example, they are
used in calculating forces and moments onaircraft, the mass flow of
petroleum through pipelines, and prediction of weather patterns.
The concept of a fluid is surprisingly general. For example, some of
the basic mathematical concepts in traffic engineering are derived from
considering traffic as a continuous fluids.
Relativity
Inspecialandgeneral relativity, some formulas for the metric
onspacetimebecome simpler if one takes the time variable to be
imaginary. (This is no longer standard in classical relativity, but
isused in an essential wayinquantum field theory.) Complex numbers are
essential tospinors, which are a generalization of thetensorsused in
relativity.
Applied mathematics
In differential equations, it is common to first find all complex
roots r of the characteristic equation of a linear differential equation
and then attempt to solve the system in terms of base functions of the
form f(t) = ert.
