# 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

Solving complex quadratic equations

Fundamental theorem of algebra

Conjugate roots

### Geometrical implications of complex numbers

Complex numbers as vectors

Adding complex numbers as vectors

Subtracting complex numbers as vectors

Scaling and rotating complex numbers as vectors

Triangle inequality for complex numbers

Roots of complex numbers

Curves and regions in the complex plane