a = 5 - i sqrt(3) ≈ 5.00000 - 1.73205 i and b = 5 + i sqrt(3) ≈ 5.00000 + 1.73205 i
a = 5 + i sqrt(3) ≈ 5.00000 + 1.73205 i and b = 5 - i sqrt(3) ≈ 5.00000 - 1.73205 i
Simplify the following:
(-(i sqrt(3)) + 5)^3 + (i sqrt(3) + 5)^3
(-(i sqrt(3)) + 5)^3 = (-(i sqrt(3)) + 5) (-(i sqrt(3)) + 5)^2:
(-(i sqrt(3)) + 5) (-(i sqrt(3)) + 5)^2 + (i sqrt(3) + 5)^3
(-(i sqrt(3)) + 5)^2 = 25 - 5 i sqrt(3) - 5 i sqrt(3) - 3 = 22 - 10 i sqrt(3):
(-(i sqrt(3)) + 5) -10 i sqrt(3) + 22 + (i sqrt(3) + 5)^3
(-i sqrt(3) + 5) (-10 i sqrt(3) + 22) = 5×22 + 5 (-10 i sqrt(3)) + -i sqrt(3)×22 + -i sqrt(3) (-10 i sqrt(3)) = 110 + -50 i sqrt(3) + -22 i sqrt(3) - 30 = -72 i sqrt(3) + 80:
-72 i sqrt(3) + 80 + (i sqrt(3) + 5)^3
(i sqrt(3) + 5)^3 = (i sqrt(3) + 5) (i sqrt(3) + 5)^2:
80 - 72 i sqrt(3) + (i sqrt(3) + 5) (i sqrt(3) + 5)^2
(i sqrt(3) + 5)^2 = 25 + 5 i sqrt(3) + 5 i sqrt(3) - 3 = 22 + 10 i sqrt(3):
80 - 72 i sqrt(3) + (i sqrt(3) + 5) 10 i sqrt(3) + 22
(i sqrt(3) + 5) (10 i sqrt(3) + 22) = 5×22 + 5×10 i sqrt(3) + i sqrt(3)×22 + i sqrt(3)×10 i sqrt(3) = 110 + 50 i sqrt(3) + 22 i sqrt(3) - 30 = 72 i sqrt(3) + 80:
80 - 72 i sqrt(3) + 72 i sqrt(3) + 80
80 - 72 i sqrt(3) + 80 + 72 i sqrt(3) = 160: SO THE ANSWER IS 160