Reflection: Connection to Prior Knowledge Trigonometric Form of Complex Numbers - Section 1: Launch and Explore

 

After working with vectors for a few days, one of my students asked what these complex numbers had to do with our work in this chapter with vectors. After processing the question I realized that it did seem like an abrupt change.

However, once we started writing the complex numbers in trigonometric form it became clear that the format was identical to vectors. Just like <rcosƟ, rsinƟ> was the general format for a vector, rcosƟ + rsinƟi is the general format for a complex number written in trig form. In both cases we are using the radius and direction angle to transition to rectangular components.

When we move on to polar equations later in the year I will be sure to come back to this important concept and tie all of these together.

  What Does This Have To Do With Vectors?
  Connection to Prior Knowledge: What Does This Have To Do With Vectors?
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Trigonometric Form of Complex Numbers

Unit 6: Additional Trigonometry Topics
Lesson 8 of 12

Objective: SWBAT find the trigonometric form of a complex number and perform operations with them.

Big Idea: Complex numbers can be represented on a graph?!

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