Pre-calc ? explain your answer and i'll mark the brainliest!
use de moivre's theorem to write the complex number in trigonometric form:

(cos π/4 + i sin π/4)3

a. 3(cos 3π/4 + i sin 3π/4)
b. (cos 3π/4 + i sin 3π/4)
c. (cos π3/64 + i sin π3/64)
d. 3(cos π/12 + i sin π/12)

 B.  (cos 3π/4 + i sin 3π/4)

Step-by-step explanation:

DeMoivre's theorem tells you the cube of a complex number is the cube of its magnitude at 3 times the angle. The given number has a magnitude of 1, so its cube will also. Three times the angle of the given number is ...

  3 × π/4 = 3π/4

so the number you're looking for among the answer choices is ...

  (cos(3π/4) +i·sin(3π/4)) . . . . matches choice B