Solution for complex eigenvalues

Thermal reactions, which take place in closed systems, do not show complex eigenvalues. In contrast, in the case of quasilinear photoreactions, such solutions cannot be excluded in principle. Complex eigenvalues always appear in pairs. In the following, a general approach to solve this problem is given for two linear independent steps of reaction (j = 2). The two eigenvalues are 

Under these conditions, the solution with respect to concentrations is given by [17] 

Taking the Erst derivative at time r = 0, the values p, and pi are determined by the following system of linear equations  

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