Complex NumbersA complex number is a number with a real and an imaginary part, usually expressed in cartesian form The polar form can also be expressed in terms of trigonometric functions using the Euler relationship 
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Euler RelationshipThe trigonometric functions are related to a complex exponential by the Euler relationship From 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.

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Polar Form, Complex NumbersThe standard form of a complex number is but 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. 
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