Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.5

Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

COS Examples

Example: $(-1 + \sqrt{3i})^3 = 8$ because $(-1 + \sqrt{3i})$ has modulus 2 and argument $120^{\circ}$.

Unpacked Content

Knowledge

Students know:
  • Complex numbers can be represented geometrically.
  • Complex numbers can be added and subtracted either geometrically or algebraically.

Skills

Students are able to:
  • Add and subtract complex numbers.
  • Find the modulus of a complex number.
  • Represent complex numbers geometrically.

Understanding

Students understand that:
  • Representing complex numbers on a rectangular coordinate system allows the use of techniques developed for real numbers to find distances and midpoints.

Vocabulary

  • Complex plane
  • Distance
  • Modulus
  • Midpoint
ALSDE LOGO