The nth roots of unity are given by cos(2πk/n) + isin(2πk/n) for k = 0, 1, ..., n-1.

If z1 and z2 subtend a right angle at the origin, then the angle between them is 90 degrees or π/2 radians.

This means that the difference in the arguments of z1 and z2 is π/2.

In terms of k, this means that (2π/n)(k2 - k1) = π/2, where k1 and k2 are the values of k corresponding to z1 and z2.

Solving for n, we get n = 4(k2 - k1).

Since k2 and k1 are integers, n must be a multiple of 4.

Therefore, n must be of the form 4m, where m is an integer.

Question

The nth roots of unity are given by cos(2πk/n) + isin(2πk/n) for k = 0, 1, ..., n-1.

If z1 and z2 subtend a right angle at the origin, then the angle between them is 90 degrees or π/2 radians.

This means that the difference in the arguments of z1 and z2 is π/2.

In terms of k, this means that (2π/n)(k2 - k1) = π/2, where k1 and k2 are the values of k corresponding to z1 and z2.

Solving for n, we get n = 4(k2 - k1).

Since k2 and k1 are integers, n must be a multiple of 4.

Therefore, n must be of the form 4m, where m is an integer.

Knowee AI · Accepted Answer

The nth roots of unity are given by cos(2πk/n) + isin(2πk/n) for k = 0, 1, ..., n-1.

If z1 and z2 subtend a right angle at the origin, then the angle between them is 90 degrees or π/2 radians.

This means that the difference in the arguments of z1 and z2 is π/2.

In terms of k, this means that (2π/n)(k2 - k1) = π/2, where k1 and k2 are the values of k corresponding to z1 and z2.

Solving for n, we get n = 4(k2 - k1).

Since k2 and k1 are integers, n must be a multiple of 4.

Therefore, n must be of the form 4m, where m is an integer.

et z1𝑧1 and z2𝑧2 be the nth𝑛𝑡ℎ roots of unity which are ends of a line segment that subtend a right angle at the origin. Then, n𝑛 must be of the form