Let α and β be the roots of the equation x 2 + 2 x + 2 = 0 , then α 15 + β 15 is equal to

Step-by-step solution

Let the two roots of x 2 + 2 x + 2 = 0 be α and β ⇒ α , β = - 2 ± 4 - 8 2 = - 1 ± i ⇒ α , β = 2 - 1 2 ± i 1 2 = 2 c o s 3 π 4 ± i s i n 3 π 4 ⇒ α 15 + β 15 = 2 c o s 3 π 4 + i s i n 3 π 4 15 + 2 c o s   3 π 4 - i s i n 3 π 4 15 = 2 15 2 c o s 45 π 4 + i s i n 45 π 4 + c o s 45 π 4 - i s i n 45 π 4 = 2.2 15 2 . c o s 45 π 4 = 2 17 2 . c o s 5 π 4 = - 2 17 2 . 1 2 = - 256