Algebra
# Roots of Unity

How many non-real solutions are there to the equation \[ x^7 = 1?\]

What is the product of the fourth roots of unity?

How many of the 12th roots of unity are not 4th roots of unity?

How many of the 5th roots of unity have positive real part?

**Note:** The real part of a complex number that can be written as \(a + bi\) for real numbers \(a\) and \(b\) is \(a\).

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