Somewhere I heard we start journey so that one day we can come back to the source.
Lately I realized that solving polynomial equation is all about bringing a set of vectors back to the source (the origin).
Think about the following polynomial equation:
c0 + c1z + c2z^2 + c3z^3 = 0
In 2D space the coefficient vectors would look like:
A solution z = r *e ^ i * theta means, scale each successive vector by 1, r, r^2, r^3 and rotate by 0, theta, 2*theta, 3*theta respectively and bring c3 back to the origin.
Visually a solution would look like:
Wow :)
Now the easy part: convince yourself that for a n-degree polynomial there are n different values of (r, theta) that will bring cn back to the home OR in other words n different polygons are possible satisfying the criteria.
Now the easy part: convince yourself that for a n-degree polynomial there are n different values of (r, theta) that will bring cn back to the home OR in other words n different polygons are possible satisfying the criteria.
