Complex numbers bridge so many concepts as learners edge into higher-level math. Here, their polar and rectangular forms link through vector notation, and the arithmetic of vectors is born. These basic math skills translate into a variety of science and integration applications, and careful introduction here of rules and patterns lays the groundwork for solid understanding of those concepts. The included homework and answer key follow the notes closely, allowing young mathematicians easy reference for independent work.

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CCSS: Adaptable
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Instructional Ideas
  • Ideal for leaving as a turnkey lesson, notes, and homework assignment for a highly qualified substitute
  • Have pairs of pupils use vector notation covered here to develop and direct one another in a scavenger hunt
  • Extend the activity by having learners create dot-to-dot pictures for one another using polar form of coordinates on the complex plane
  • Create a cross-curricular lesson with a physics unit on applying vectors and mapping motion
Classroom Considerations
  • Notes, homework, and homework key are included to match main presentation in the additional resources
  • Due to the high amount of content covered, consider posting the lesson and notes online for learners to review and use as models while completing homework 
  • Main resource presentation would make an excellent interactive whiteboard lesson, with steps revealed as problems are worked and discussed
  • This resource is only available on an unencrypted HTTP website. It should be fine for general use, but don’t use it to share any personally identifiable information
  • Notes include a summary of key strategies at the start of each section
  • Presentation, notes, and homewark are all closely aligned
  • Examples and problems build gradually in difficulty and complexity
  • None