ind the complex roots of 81[cos(3pi/8) + i sin(3pi/8)]. Part I: Find the fourth root of 81. Part II: Divide the angle in the problem by 4 to find the first argument. Part III: Use the fact that adding 2π to the angle (3pi/8) produces the same effective angle to generate the other three possible angles for the fourth roots. Be sure that your angles lie between 0 and 2π. Part IV: Find all four of the fourth roots of the original given info. Express your answers in polar form (cos theta + i sin theta).

Question

ind the complex roots of 81[cos(3pi/8) + i sin(3pi/8)].  Part I: Find the fourth root of 81.   Part II: Divide the angle in the problem by 4 to find the first argument.  Part III: Use the fact that adding 2π to the angle (3pi/8) produces the same effective angle to generate the other three possible angles for the fourth roots. Be sure that your angles lie between 0 and 2π.  Part IV: Find all four of the fourth roots of the original given info. Express your answers in polar  form (cos theta + i sin theta).