Complex Numbers and Functions
The Complex Number System
Basic Operations
For and :
Modulus and Argument
Polar Form
where and .
Euler's Formula
De Moivre's Theorem
Conjugate
Division
Complex Exponential
Complex Logarithm
Complex Power
Elementary Functions
Sine and Cosine: ,
Hyperbolic Functions: ,
Roots of Unity
Fundamental Theorem of Algebra
Every non-constant polynomial with complex coefficients has a root in .