Therefore, the poles and zeroes of the transfer function will either be real or occur in complex conjugate pairs.
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The asterisk denotes complex conjugate.
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It may also occur that such a multiple linear factor corresponds to two complex conjugate branches, and does not corresponds to any infinite branch of the real curve.
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Where the wave equation is represented as a complex vector, the probability will be extracted from the absolute value of an inner-product of the coefficient matrix and its complex conjugate.
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Geometric representation of z and its conjugate in the complex plane.
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The complex analytic inverse map is conformal and its conjugate, circle inversion, is anticonformal.
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In the complex case, one can check also that the bilinear form is linear over i in one argument, and conjugate linear in the other.