Abstract
General complex Lorentz transformations and complex conformal rescalings with independent conformal factors theta and theta can be represented as elements of the group GL(2,C)(X)GL(2,C). The corresponding general transformation laws for directional derivatives, spin coefficients and components of the electromagnetic field (the Weyl tensor and the Ricci tensor) are obtained. For the sake of conciseness they are presented in matrix form. The 'diagonal case', which includes complex boost rotations and standard conformal rescalings (but not null rotations), is singled out for special attention.
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