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  • Separating the real and imaginary parts of the complex dielectric permittivity yields:
  • In which the imaginary parts offset each other leaving a real-valued expression.
  • The real and imaginary parts of \ gamma can be computed as
  • The entries of the corresponding eigenvectors therefore may also have non-zero imaginary parts.
  • Capacitive admittances have positive imaginary parts and inductive admittances have negative imaginary parts.
  • Complex samples of real-valued sinusoids have zero-valued imaginary parts and do exhibit folding.
  • Relative permittivity is a complex-valued; its real and imaginary parts are denoted as:
  • The real part of a complex number is, and its imaginary part is.
  • In this approach, \ psi is either the real or imaginary part of:
  • The imaginary part of a response function describes how a system driving force.
  • Let ? be a complex number with strictly positive imaginary part.
  • Capacitive admittances have positive imaginary parts and inductive admittances have negative imaginary parts.
  • By taking linear combinations, the real and imaginary parts of are each solutions.
  • In fact if the imaginary part of is positive, then is invertible since
  • Which has a pole in z = 0.5 ( zero imaginary part ).
  • The imaginary part is a sine wave with perpendicular polarisation to the cosine wave.
  • Which I can't separate into the real and imaginary part.
  • Are called the imaginary parts of the complex amplitude represented by \ widehat a.
  • In complex analysis, the hyperbolic functions arise as the imaginary parts of sine and cosine.
  • A complex number is called arithmetical if its real and imaginary parts are both arithmetical.
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