Find Imaginary Solutions: Imaginary Zeros Interactive

The Fundamental Theorem of Algebra tells us that any polynomial of degree n has n roots. At first, this may seem like a very convenient theorem but wait, what about counterexamples!? The function f(x) = x² + 1 clearly has no roots along the x-axis and we are told to believe that this function has 2. Does this mean that the Fundamental Theorem of Algebra is false?

In the interactive, students will:

• see two graphs on the complex plane.
  • The vertical axes are imaginary and the horizontal axes are real.
  • The vectors in the complex plane that compose the blue circle are mapped to the red circle in the complex plane through the function f(x) = x² + 1.
  • The vectors in the blue circle have been highlighted to see their mapping in the red circle.
• move the red point to see how the red circle maps to the complex plane.