High School · The Complex Number System

CCSS.MATH.CONTENT.HSN.CN.C.9

(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Read this standard on the official Common Core site

Lessons that teach this standard

• The Fundamental Theorem of Algebra

  A polynomial of degree n has exactly n complex zeros, counted with multiplicity. Use that count and conjugate pairs to find every zero and build polynomials.

• Quadratic Equations with Complex Solutions

  How the quadratic formula gives complex solutions when the discriminant is negative, why they come in conjugate pairs, and what the Fundamental Theorem of Algebra says.

• De Moivre's Theorem and Roots of Complex Numbers

  Raise a complex number to a power by raising its length and multiplying its angle, then reverse the rule to find all n of its nth roots, evenly spaced on a circle.