Students will discover the complex conjugate root theorem by working this problem: Use properties of complex conjugates to show that if \(\alpha\) is a complex root of a quadratic equation \(ax^2 + bx + c = 0,\) with \(a, b, c\) being real coefficients, then so is \(\overline{\alpha}.\) Does this generalize to higher degree polynomials? Here's a fantastic explanation.
Conclude by giving your students these challenges:
Problem: What are the areas of the squares you can make on a \(4 \times 4\) Geoboard? (source).
Solution: \(1, 2, 4, 5, 9\)
