Question

4 part question

Answer 1

well part I is pretty straightforward, what's the fourth root of 81?

Answer 2

3

Answer 3

good

then for part II just divide the angle 3pi/8 by 4

Answer 4

3pi/32

Answer 5

good

then for part III they basically just want you to solve

[3pi/8 + 2pi*k]/4

for k = 1,2,3

(normally we would start with k = 0 but we already covered that in part II)

Answer 6

[3pi/8 + 2pi*1]/4=19pi/32
[3pi/8 + 2pi*2]/4=35pi/32
[3pi/8 + 2pi*3]/4=52pi/32

Answer 7

good

then for part IV you just want to find all four roots

r^(1/n) * [cos(theta) + i*sin(theta)]

by plugging in one theta value at a time, starting with the first theta value 3pi/32

if you recall, we calculated the 4th root of 81 to be 3, so r^(1/n) = 3

Answer 8

3 * [cos(3pi/32) + i*sin(3pi/32)]
3 * [cos(19pi/32) + i*sin(19pi/32)]
3 * [cos(35pi/32) + i*sin(35pi/32)]
3 * [cos(52pi/32) + i*sin(52pi/32)]

Answer 9

good so those are your roots and that's it