Question

Let d and e be two roots of the equation x2 + 2x + 2 = 0, then d15 + e15 is equal to :

Answer 1

(-1 + ι)¹⁵ + (-1 - ι)¹⁵

Step-by-step explanation:

Let d and e be two roots of the equation x2 + 2x + 2 = 0, then d15 + e15 is equal to

x² + 2x + 2 = 0

d & e are roots

d + e = - 2  ( sum of roots)

de = 2  (product of Roots)

roots =  (- 2 ± √(4-8))/2

= -1 ± ι

d = -1 + ι

e = -1 - ι

d¹⁵ + e¹⁵ = (-1 + ι)¹⁵ + (-1 - ι)¹⁵