DeMoivre's Theorem: Visualization
- Author:
- Brian Sterr
Move the labeled point to any complex number, , on the polar grid above.
The red curve shows all of the powers of that number. To see the first powers, click on the checkbox.
You can adjust from 1 to 20. You can also show the segments from 0 to each point to see the relationship between their arguments.
Interesting things to explore:
1. What happens if ?
2. What happens if the number is on the real axis ( or )?
3. What if ?
4. What number is always on the red curve, no matter where you drag ?