Trigonometry/Trigonometric Form of the Complex Number

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where

  • i is the imaginary number
  • the modulus
  • the argument is the angle formed by the complex number on a polar graph with one real axis and one imaginary axis. This can be found using the right angle trigonometry for the trigonometric functions.

This is sometimes abbreviated as and it is also the case that (provided that is in radians). The latter identity is called Euler's formula.

Euler's formula can be used to prove DeMoivre's formula: This formula is valid for all values of n, real or complex.