### Introduction to complex numbers

Definition of imaginary and complex numbers

### Arithmetic of complex numbers

Addition, subtraction and multiplication of complex numbers

Complex conjugates and dividing complex numbers

Square roots of complex numbers

### Geometric and other representations of complex numbers

Polar form and argument properties

Exponential form of a complex number

Multiplication and division in polar form

### Solving equations with complex numbers

Trigonometric identities with de Moivre’s theorem

Solving complex quadratic equations

Fundamental theorem of algebra

### Geometrical implications of complex numbers

Adding complex numbers as vectors

Subtracting complex numbers as vectors

Scaling and rotating complex numbers as vectors