# Complex numbers

### Introduction to complex numbers

Types of numbers

Definition of imaginary and complex numbers

Equality of complex numbers

### Arithmetic of complex numbers

Addition, subtraction and multiplication of complex numbers

Complex conjugates and dividing complex numbers

Complex conjugate properties

Square roots of complex numbers

### Geometric and other representations of complex numbers

Complex plane

Modulus of a complex number

Argument of a complex number

Polar form and argument properties

Exponential form of a complex number

Multiplication and division in polar form

### Solving equations with complex numbers

De Moivre’s theorem

Trigonometric identities with de Moivre’s theorem

Fundamental theorem of algebra

Conjugate roots

### Geometrical implications of complex numbers

Complex numbers as vectors