INDEX
Numbers and Sets
Exponentiation
Algebraic Transformations
Algebraic Equations and Inequalities
Functions
Discrete Algebra
Basic Formulas
Graphics of Basic Functions
Complex Numbers
Ship 2

Definition and Properties

Basic Definitions

Algebraic Operations

Complex Conjugation

Trigonometrical and Exponential Forms

The Complex Plane

Complex Numbers in Polar Coordinate System

The Euler Formula
  Trigonometric Applications
  Algebraic Applications

Powers of Complex Numbers

Complex Roots

Algebraic Applications of the Euler Formula
Key Topics Remaining:   Complex Roots
  1. Let  and  . Then

.

Therefore,

| z | = | z1 | · | z2 |

and

arg( z ) = arg( z1) + arg( z2).

  1. Likewise, if   is divided by    then


and
.

  1. The integer power n of a complex number  can be written in closed form as follows:

.

This formula is known as the DeMoivre Identity.

Examples
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