Question

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Answer 1

each root can be found with the equation

cos(2pi*k/n) + i*sin(2pi*k/n)

n = the number of roots (since they are asking for the seventh roots, n = 7)

k is an integer, start with 0, 1,2,... and keep going to k = 6

that will give you a list of 7 roots in polar form

Answer 2

as for the drawing it's just seven lines radiating from the origin and extending to 1, make sure they are evenly spaced

Answer 3

can use desmos as reference

https://www.desmos.com/calculator/hrji4ser8l

Answer 4

okay what points d i graph the lines on like imsonfused

Answer 5

after you plug in k = 0,1,2,3,4,5, and 6 to this equation

cos(2pi*k/n) + i*sin(2pi*k/n)

you should end up with 7 sets of points, plot those on the graph such that they are exactly 1 unit away from the origin and evenly spaced from each other

Answer 6

remember that cos(theta) represents x and sin(theta) represents y

Answer 7

anyway i'm super tired im going to to bed

Answer 8

like this

Answer 9

there must be seven distinct points on the graph

Answer 10

notice how this graph has the seven roots of unity plotted as black dots