Imaginary unit
The imaginary unit, , is the fundamental component of all complex numbers. In fact, it is a complex number itself. It has a magnitude of 1, and can be written as .
Contents
Trigonometric function cis
- Main article: cis
The trigonometric function $\cis x$ (Error compiling LaTeX. Unknown error_msg) is also defined as or .
Series
When is used in an exponential series, it repeats at every fifth term:
This has many useful properties.
Use in factorization
is often very helpful in factorization. For example, consider the difference of squares: . With , it is possible to factor the otherwise-unfactorisable into .
Problems
Introductory
- Find the sum of (Source)