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 . Any complex number can be expressed as for some real numbers and .
Trigonometric function cis
- Main article: cis
The trigonometric function is also defined as or .
When is used in an exponential series, it repeats at every four terms:
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 .
- The equation has complex roots with argument between and in the complex plane. Determine the degree measure of . (Source)
- Let and with no real roots. If , show that . <url>viewtopic.php?t=78260 (Source)</url>