A complex number z is called a nth root of unity if z^n = 1. a.) How many nth roots of unity are there? (Apply the Fundamental Theorem of Algebra) b.) Write the nth roots of unity {z_k} (all of them) in polar form, i.e. z_k = re^(i*theta) for what r and theta?
There are an n-number of them. z^n = 1 z^n = (1 + 0i) z^n = cos(2pi * k) + i * sin(2pi * k) (let k be an integer) z = (cos(2pi * k) + i * sin(2pi * k))^(1/n) z = cos(2 * pi * k / n) + i * sin(2 * pi * k / n)