Let α and β be the roots of the equation x 2 + 2 i - 1 = 0 . Then, the value of α 8 + β 8 is equal to

Step-by-step solution

Since α and β are the roots of the equation x 2 + 2 i - 1 = 0 so α 2 = - 2 i + 1 = β 2 ⇒ α 4 = - 2 i + 1 2 = 4 i 2 + 1 - 4 i = - 3 - 4 i ⇒ α 8 = - 3 - 4 i 2 = - 7 + 24 i Similarly, β 8 = - 7 + 24 i ∴ α 8 + β 8 = - 14 + 48 i = 50