Studying Mathematics Thread

[robvalue]

Another interesting thing about complex numbers is that you sometimes get extra solutions you wouldn't normally think of.

For example, consider

x^3 = 1

What's the solution?

x = 1

Obviously. But there's also two other solutions, if we allow x to be complex. They fall on the unit circle drawn in the complex plane around the origin, at angles 120 and 240 degrees from the positive real axis. Multiplying those numbers by themselves rotates them around the origin, so 3 * 120 = 360 and 3 * 240 = 720 leaving you back on the positive real axis at 1.