Complex NumbersA complex number is a number with a real and an imaginary part, usually expressed in cartesian formComplex numbers can also be expressed in polar form The polar form can also be expressed in terms of trigonometric functions using the Euler relationship 
Index Complex numbers 
HyperPhysics****HyperMath*****Algebra  Go Back 
Euler RelationshipThe trigonometric functions are related to a complex exponential by the Euler relationshipFrom these relationships the trig functions can be expressed in terms of the complex exponential: This relationship is useful for expressing complex numbers in polar form, as well as many other applications.

Index Complex numbers  
HyperPhysics****HyperMath*****Algebra  Go Back 
Polar Form, Complex NumbersThe standard form of a complex number isbut this can be shown to be equivalent to the form which is called the polar form of a complex number. The equivalence can be shown by using the Euler relationship for complex exponentials. 
Index Complex numbers 
HyperPhysics****HyperMath*****Algebra  Go Back 