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Vectors, the Complex Plane, and Polar Coordinates: Structured Study Notes

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Geometric Vectors

  • Multiplying Vectors By Scalars Example 1
    03:12
  • Multiplying Vectors By Scalars
    05:05
  • Adding Vectors Geometrically
    05:29

Vectors in Component Form

  • Finding Magnitude of a Vector Example 1
    02:26
  • Position Vectors & Component Form
    03:55
  • Algebraic Operations on Vectors Example 1
    03:11

Direction of a Vector

  • Finding Components from Direction and Magnitude
    04:55
  • Finding Direction of a Vector
    05:13
  • Finding Direction of a Vector Example 1
    04:19

Unit Vectors and i & j Notation

  • Unit Vector in the Direction of a Given Vector Example 1
    02:17
  • i & j Notation
    06:01
  • Unit Vector in the Direction of a Given Vector Example 2
    05:21

Dot Product

  • Introduction to Dot Product
    05:40
  • Find the Angle Between Vectors
    04:33

Polar Coordinate System

  • Intro to Polar Coordinates
    05:32
  • Determining Different Coordinates for the Same Point
    6:02
  • Intro to Polar Coordinates Example 1
    02:13

Convert Points Between Polar and Rectangular Coordinates

  • Convert Points from Rectangular to Polar Example 1
    2:21
  • Convert Points from Rectangular to Polar
    6:58
  • Convert Points from Polar to Rectangular
    06:17

Convert Equations Between Polar and Rectangular Forms

  • Convert Equations from Rectangular to Polar
    3:37
  • Convert Equations from Polar to Rectangular Example 2
    3:03
  • Convert Equations from Polar to Rectangular
    6:50

Polar Form of Complex Numbers

  • Converting Complex Numbers from Polar to Rectangular Form
    03:58
  • Complex Numbers In Polar Form
    04:47

Products and Quotients of Complex Numbers

  • Quotients of Complex Numbers in Polar Form
    03:40
  • Products of Complex Numbers in Polar Form
    04:46

Powers of Complex Numbers (DeMoivre's Theorem)

  • Complex Roots
    07:37
  • Complex Roots Example 1
    07:55
  • Powers Of Complex Numbers In Polar Form (DeMoivre's Theorem)
    03:41