Calculate radius, diameter, and circumference (Advanced)

What you'll learn

• Identify complex conjugate pairs given a quadratic or polynomial equation with real coefficients, and verify that they are roots of the equation.
• Solve quadratic equations with real coefficients that have complex roots, expressing the solutions in the form a + bi and a - bi, and demonstrating understanding of the complex conjugate theorem.
• Explain how the Complex Conjugate Theorem guarantees that if a polynomial with real coefficients has a complex root a + bi, then its conjugate a - bi must also be a root, justifying the reasoning with examples.
• Apply the Complex Conjugate Theorem to construct a polynomial equation with real coefficients given a set of roots, including at least one complex root, expressing the polynomial in standard form.