nth Roots in the Complex Plane

Topic:
Root
The green points arranged around the circle in the right-hand pane are the nth roots of the blue point, c, in the left-hand pane. The slider in the left-hand pane allows you to see the nth roots for other values of n. The circle in the right-hand pane shows the magnitudes of the nth roots.
  1. What effect does changing n have on the roots?
  2. Under what circumstances are there two real roots?
  3. Under what circumstances are there two pure imaginary roots?
  4. Are there any circumstances when there are no real roots? One real root? Three real roots?