If a and b are real numbers such that (2+α)4=a+bα, where α=-1+i32, then a+b is equal to:

(2+α)4=a+bαα=-12+i32=ei2π3⇒(2+ω)4=a+bω1+ω=-ω22+ω=1-ω21-ω24=a+bω1-4ω2+6ω4-4ω6+ω8=a+bω1-4ω2+6ω-4+ω2=a+bω6ω-3ω2-3=a+bω9ω-3ω+ω2-3=a+bω9ω+3-3=a+bωa=0,b=9so, a + b = 9