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

MA19.PRE.3

Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

Unpacked Content

Knowledge

Students know:
  • In the complex plane the horizontal axis is the real axis (a) and the vertical axis is the imaginary axis (b).
  • Trigonometric techniques for finding measures of angles and coordinates on the unit circle.
  • The characteristics of the polar coordinate system.
  • Techniques for plotting polar coordinates.

Skills

Students are able to:
  • Use trigonometry to find the measures of angles and coordinates on the unit circle.
  • Use the Pythagorean Theorem to find the lengths of sides of a right triangle.
  • Convert between polar and rectangular forms.
  • Plot polar coordinates.

Understanding

Students understand that:
  • A complex number (a+bi) can be graphed in a rectangular coordinate system as (a, b).
  • A complex number may be represented in the plane using equivalent polar and rectangular coordinates.
  • Different representations of a complex number may be more useful for various purposes.

Vocabulary

  • Complex plane
  • Polar form
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