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The simple classical theory employed in the analysis of electromagnetic waves propagating through an ionized gas is not sufficiently general to take into account the variation of the complex conductivity of the plasma with the magnitude of the impressed EM field. Problems of this nature arise when it becomes necessary to transmit radar signals of high energy density through the ionized shock wave produced by a hypersonic vehicle. The exact theory of conductivity developed by Margenau is for impressed, relatively high field strengths too difficult to handle from an analysis and computational standpoint. By making two simplifying assumptions in the general velocity distribution function and graphically interpolating between them, two relations, one nearly exact and one employing the simple theory, are obtained for the conductivity. The accuracy of these relations is then examined analytically for a typical case, and graphical comparisons between the methods are made. Effects of neglecting Coulomb interactions and higher order components in the velocity distribution function are considered briefly. For an example, the complex conductivity of a typical ionized shock wave as a function of field strength and frequency is calculated and plotted.