Suppose a(2+i)^4 + b(2+i)^3 + c(2+i)^2 + b(2+i) + a = 0 where a,b,c are integers whose greatest common divisor is 1. Determine the absolute

Suppose a(2+i)^4 + b(2+i)^3 + c(2+i)^2 + b(2+i) + a = 0
where a,b,c are integers whose greatest common divisor is 1.
Determine the absolute value of c.