complex numbers

• How Do You Find the Square Root of a Negative Number?
  A negative real number has no real square root. In the complex numbers, its principal square root is i times the square root of its positive opposite.
• Why Are Complex Numbers Numbers but 2D Vectors Usually Aren’t?
  Complex numbers are numbers because they have a consistent arithmetic structure. A 2D vector becomes one if you define suitable multiplication.
• Why Can’t a Negative Number Have a Real Square Root?
  No real number squares to a negative value, but complex numbers provide square roots: for a > 0, the roots of −a are ±i√a.