Question

If α, β are the roots of the equation x² - 2x + 4 = 0. Find the value of αⁿ + βⁿ.

(1) 2ⁿ⁺¹ cos(nπ/3). 

(2) 2ⁿ cos(nπ/3). 

(3) 2ⁿ⁺¹ sin(nπ/3). 

(4) none of these.    

Answer 1

x² - 2x + 4 = 0

⇒ αⁿ = 2ⁿ (cos nπ/3 + i sin nπ/3), βⁿ = 2ⁿ (cos nπ/3 - i sin nπ/3)