a) The roots are (6√3 + 6i) and (-6√3 - 6i) \ \

Therefore (6√3 + 6i) (-6√3 - 6i) \ \

= 6√3(-6√3) + 6√3( - 6i) + 6i(-6√3) + 6i( - 6i) \ \

= -108 - 36(-1) \ \

= 108 + 36 = 144  ≠  -18 + 18√3i \ \

b) The roots are (6 + 6√3i) and (-6 - 6√3i) \ \

Therefore (6 + 6√3i) (-6 - 6√3i) \ \

= 6(-6) + 6( - 6√3i) + 6√3i(-6) + 6√3i( - 6√3i) \ \

= -36 -36√3i - 36√3i - 36(3)(i)²  \ \

= -36 -72√3i -108(-1) \ \

= -36 - 72√3i + 108 \ \

= 72 - 72√3i ≠  -18 + 18√3i \ \

c) The roots are (3√3 + 3i) and (-3√3 - 3i) \ \

Therefore (3√3 + 3i) (-3√3 - 3i) \ \

= 3√3(-3√3) + 3√3( - 3i) + 3i(-3√3) + 3i( - 3i) \ \

= -9(3) - 9i√3 - 9i√3 - 9(i)² \ \

= -27 - 18i√3 - 9(-1) \ \

= -27 - 18i√3 + 9 \ \

= -18 - 18i√3 ≠  -18 + 18√3i \ \

d) The roots are (3 + 3√3i) and (-3 - 3√3i) \ \

Therefore (3 + 3√3i) (-3 - 3√3i) \ \

= 3(-3) + 3( - 3√3i) + 3√3i(-3) + 3√3i( - 3√3i) \ \

= -9 - 9√3i - 9√3i - 9(3)(i)² \ \

= -9 - 18√3i - 27(-1) \ \

= -9 - 18√3i + 27 \ \

= 18 - 18√3i  ≠  -18 + 18√3i \ \