# Complex Fibonacci Residues

Complex Fibonacci Residues

The Fibonacci numbers are defined by the recurrence . The sequence is periodic for any moduli . Fibonacci numbers have been generalized to real and complex numbers. The plots show the norm, argument, real and imaginary parts modulo real numbers. A further generalization is to take the Fibonacci numbers modulo a complex number.

f(n)=f(n-1)+f(n-2)

f(n)modm

m