Complex numbers

• What Is the Cube Root of a Negative Number?
  A negative number has a negative real cube root; over the complex numbers, it also has two nonreal cube roots.
• How to Find the Real and Imaginary Parts of a Polynomial
  Find a polynomial’s real and imaginary parts by substituting z = x + iy, expanding, and collecting terms; verify the result with SymPy.
• Find z Given Arg(z + 1) = π/6 and Arg(z − 1) = 2π/3
  The two argument conditions define rays from −1 and 1. Their intersection is z = 1/2 + (√3/2)i, as direct substitution verifies.
• 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.