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

Step-by-step solution

2 + α 4 = a + b α 4 + α 2 + 4 α 2 = a + b α Now using, α = - 1 + i 3 2 ⇒ 2 α + 1 2 = i 3 2 ⇒ α 2 = - 1 + α So, a + b α = 4 - α - 1 + 4 α 2 a + b α = 3 + 3 α 2 = 9 1 + 2 α + α 2 a + b α = 9 1 + 2 α + - 1 - α = 9 α ⇒ a = 0 ,   b = 9 ⇒ a + b = 9