If a and b are real numbers such that 4 (2 ) , +a = + a a b where 1 3 , 2 – + i a = then a + b is equal to :

Question:
If $a$ and $b$ are real numbers such that $(2+\alpha)^{4}=a+b \alpha$, where $\alpha=\frac{-1+i \sqrt{3}}{2}$, then $a+b$ is equal to :

Correct Option: 1

JEE Main Previous Year 1 Question of JEE Main from Mathematics Complex Numbers and Quadratic Equations chapter.