Combinatorics
Complex roots are solutions to polynomial equations that involve imaginary numbers, typically expressed in the form 'a + bi', where 'a' and 'b' are real numbers, and 'i' is the imaginary unit satisfying $i^2 = -1$. In the context of linear recurrence relations with constant coefficients, complex roots arise when the characteristic equation of the relation has no real solutions. Understanding complex roots is essential as they affect the behavior of the solutions to recurrence relations, particularly in their oscillatory nature and growth rates.
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