Real or Complex ???

Algebra Level 4

If \(a,b,c\) are real numbers in the polynomial \(P(Z)=2Z^{4} + aZ^{3} + bZ^{2} + cZ + 3,\) and two roots of the equation \(P(Z)=0\) are \(2\) and \(i,\) what is the value of \(a?\)