Find the 6th complex roots of √3 + i.
The Attempt at a Solution
When k=0, z = 2^1/6(cos(π/36)+isin(π/36)),
When k=1, z = 2^1/6(cos(13π/36)+isin(13π/36)),
When k=2, z = 2^1/6(cos(25π/36)+isin(25π/36)),
When k=3, z = 2^1/6(cos(37π/36)+isin(37π/36)),
When k=4, z = 2^1/6(cos(49π/36)+isin(49π/36)),
When k=5, z = 2^1/6(cos(61π/36)+isin(61π/36)).
I just want help with plotting these roots on the complex plane. So, I am just wondering, are all roots of unity on the complex plane the same, regardless of the equation? By this, I mean, are the position of the roots the same, regardless of what the equation is?