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Mathematics · Grade 11

Complex Numbers and Quadratic Reasoning

Learners meet the imaginary unit i, do arithmetic with complex numbers (including powers of i, conjugates and division), and plot complex numbers in the complex plane. They solve every quadratic equation, including those with complex solutions, derive the quadratic formula by completing the square, and use the Fundamental Theorem of Algebra and conjugate pairs to count and find polynomial zeros. An optional honors lesson explains why complex zeros of real polynomials come in pairs.

  • 5 lessons
  • About 130 minutes
  • Complex numbers check: 11 questions
  • Ways to answer: choose an answer, plot points, match pairs, type a number, put in order and sort into groups
See plans Included with Family, Teacher and School plans. Open in PlayOwl

What learners will discover

  • Perform arithmetic with complex numbers (including powers of i, conjugates and division) and represent them in the complex plane with their modulus.
  • Solve quadratic equations with real or complex solutions and use the discriminant to classify the solutions.
  • Derive the quadratic formula by completing the square, justifying each step.
  • Apply the Fundamental Theorem of Algebra and the conjugate pair theorem to count and find the zeros of polynomials.

Lessons

  1. Complex number arithmetic and the complex plane 7 steps5 practiceabout 32 min
  2. Solving every quadratic 6 steps3 practiceabout 28 min
  3. Deriving the quadratic formula 5 steps2 practiceabout 25 min
  4. The Fundamental Theorem of Algebra 6 steps4 practiceabout 30 min
  5. Going further (honors): why conjugates pair up 3 steps1 practiceabout 15 min
  6. Complex numbers check 11 questions at the end

Keep exploring

More 11th grade math

Guide for grown-ups