# Complex Numbers

A complex number is a number with a real and an imaginary part, usually expressed in cartesian form a + jb = + j

Complex numbers can also be expressed in polar form A = , θ = radians =°

The polar form can also be expressed in terms of trigonometric functions using the Euler relationship Index

Complex numbers

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# Euler Relationship

The 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.

Applications:
 Traveling waves
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Complex numbers

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# Polar Form, Complex Numbers

The 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. Index

Complex numbers

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