Find 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

Find 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).