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Lesson Plan: The 𝑛th Roots of Unity Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use de Moivreโ€™s theorem to find the ๐‘›th roots of unity and explore their properties.


Students will be able to

  • find the ๐‘›th roots of unity and understand the derivation of the formula using de Moivreโ€™s Theorem,
  • plot the ๐‘›th roots of unity on an Argand diagram and understand the geometric properties of this diagram,
  • solve problems using the properties of the ๐‘›th roots of unity,
  • understand the relationship between ๐‘›th and ๐‘›th roots of unity where ๐‘› and ๐‘› share a factor,
  • understand the definition of a primitive root of unity.


Students should already be familiar with

  • de Moivreโ€™s theorem,
  • different forms of complex numbers including Cartesian (algebraic , rectangular), polar (trigonometric), and exponential,
  • representing a complex number on an Argand diagram.


Students will not cover

  • ๐‘›th roots of an arbitrary complex number.

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