Complex Numbers

  • James B. Seaborn


Complex numbers play a very useful role in applied mathematics. As an example, let us consider the behavior of a particle of mass m constrained to move in one dimension under the influence of an elastic force,
$$F\, = \, - kx$$
where x is the displacement of the particle from its equilibrium position andk is a constant. This relation is known as Hooke’s law. From Newton’s second law of motion (F = ma), we have
$$- kx\, = \,m\frac{{d^2 x}}{{dt^2 }}\,$$
$$\,\frac{{d^{2x} }}{{dt^2 }}\, + \,\frac{k}{m}x\, = \,0.$$


Imaginary Part Complex Number Complex Variable Equilibrium Position Linear Differential Equation 
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Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • James B. Seaborn
    • 1
  1. 1.Department of PhysicsUniversity of RichmondUSA

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