nth Roots in the Complex Plane
- Albert Schueller
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.
- What effect does changing n have on the roots?
- Under what circumstances are there two real roots?
- Under what circumstances are there two pure imaginary roots?
- Are there any circumstances when there are no real roots? One real root? Three real roots?