A. Use de Moivre’s formula to verify that the 5th roots of unity form a group under complex...

Question

A. Use de Moivre’s formula to verify that the 5th roots of unity form a group under
complex multiplication, showing all work.

de Moivre’s theorem is:

zn = [cos(2k) + i sin(2k)]

z = 11/n = [cos(2k) + i sin(2k)]1/n

11/n = (cos
n
k2
) + i (sin
n
k2
)

for n = 5, k = 0,1,2,3,4

Therefore,

(cos
5
02
) + i (sin
5
02
) = cos 0 + i sin 0 = 1
(cos
5
12
) + i (sin
5
12
) = cos(2/5) + i sin(2/5)
(cos
5
22
) + i (sin
5
22
) = cos(4/5 + i sin(4/5)
(cos
5
32
) + i (sin
5
32
) = cos(6/5) + i sin(6/5)
(cos
5
42
) + i (sin...

Robert · Accepted Answer

A. Use de Moivre’s formula to verify that the 5th roots of unity form a group under 
complex multiplication, showing all work. 
 
de Moivre’s theorem is: 
 
zn = [cos(2k) + i sin(2k)] 
 
z = 11/n = [cos(2k) + i sin(2k)]1/n 
 
11/n =  (cos
n
k2
) +  i (sin 
n
k2
) 
 
for n = 5, k = 0,1,2,3,4 
 
Therefore,

A. Use de Moivre’s formula to verify that the 5th roots of unity form a group under complex multiplication, showing all work. I have used De Moivre's formula used to determine the 5th roots of unity....

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