Lesson Plan: Arbitrary Roots of Complex Numbers Mathematics

This lesson plan includes the objectives and prerequisites of the lesson teaching students how to use de Moivre’s theorem to find the 𝑛th roots of a complex number and explore their properties.

Objectives

Students will be able to

  • find the 𝑛th roots of a complex number using algebraic methods,
  • find the 𝑛th roots of a complex number using de Moivre’s theorem,
  • represent the 𝑛th roots of complex numbers on an Argand diagram,
  • make links between the roots of unity and the roots of complex numbers,
  • solve geometric applications on 𝑛th roots of complex numbers.

Prerequisites

Students should already be familiar with

  • writing complex numbers in algebraic (rectangular and Cartesian), polar (trigonometric), and exponential (Euler’s) forms,
  • representing different forms of complex numbers on an Argand diagram,
  • roots of unity,
  • primitive roots of unity.

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