Extend polynomial identities to complex numbers

What you'll learn

1. Factor expressions of the form a^2 + b^2 using complex numbers: a^2 + b^2 = (a + bi)(a - bi).
2. Write the factored form of any quadratic with real coefficients using its complex roots.
3. Verify polynomial factorizations by expanding the complex factors.
4. Recognize that every polynomial with real coefficients factors into linear factors over the complex numbers.

Prerequisites

• Add, subtract, and multiply complex numbers