N-CN - Domain

The Complex Number System

High School Number & Quantity · Common Core State Standards · Common Core 2010

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Vocabulary
complex numbercomplex planearithmetic operationsreal coefficientsquadratic equationspolynomial identitiesFundamental Theorem of Algebramodulusconjugaterectangular formpolar form
Skills
  • Know (there is a complex number i such that i² = –1) #dok1
  • Know (every complex number has the form a + bi with a and b real) #dok1
  • Identify (rectangular and polar forms of complex numbers) #dok1
  • Use (relation i² = –1 to add, subtract, and multiply complex numbers) #dok2
  • Use (conjugates to find moduli and quotients of complex numbers) #dok2
  • Explain (why rectangular and polar forms represent the same number) #dok2
  • Solve (quadratic equations with real coefficients that have complex solutions) #dok3
  • Calculate (distance and midpoint in the complex plane using modulus and average) #dok3
  • Extend (polynomial identities to complex numbers) #dok4
Learning Targets
  • I can identify complex numbers and their forms. #dok1
  • I can recognize the complex number i. #dok1
  • I can use the properties of complex numbers to perform operations. #dok2
  • I can interpret the relations between rectangular and polar forms of complex numbers. #dok2
  • I can solve quadratic equations involving complex solutions. #dok3
  • I can calculate the distance and midpoint of complex numbers on the complex plane. #dok3
  • I can extend polynomial identities to include complex numbers. #dok4
Big Ideas
  • Complex numbers are an extension of the real numbers and can be used to solve equations that have no real solution.
  • The operations and representations of complex numbers in different forms allow for diverse applications in mathematics.
Essential Questions
  • What is a complex number and how is it structured?
  • How do the rectangular and polar forms of a complex number relate?
  • How can we use complex numbers to solve real-world problems?
  • In what ways do polynomial identities extend when including complex numbers?
  • Why is understanding the operations on the complex plane important?