Complex Numbers Revision

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Complex Numbers

first things first....  (http://dc442.4shared.com/img/5Rf5JxqP/CodeCogsEqn__3_.gif) This is just an assumption that (http://dc442.4shared.com/img/5Rf5JxqP/CodeCogsEqn__3_.gif) is a number that exists and is usually represented as "i" or "j".

Terminology:

Any multiple of (http://latex.codecogs.com/gif.download?i) is an "imaginary number" - eg (http://latex.codecogs.com/gif.download?26i) is an imaginary number.

A number which is (or can be ) simplified to the form: (http://latex.codecogs.com/gif.download?a%20+%20bi)  is a "complex number" eg (http://latex.codecogs.com/gif.download?2+3i) is a complex number.

where 

a is the real part.

b is the imaginary part.

Argand Diagram.

Complex numbers can be represented on a graph which is called an "Argand Diagram".

[Can't draw graphs here so please bear.]

Remind your self of the cartesian coordinates... (x, y)

To exactly define a point on the graph, you need to have to numbers: x and y coordinate.

Likewise a complex number can be represented as a point on the argand diagram. By convention, the real part is the horizontal distance from the origin (like x coordinate on cartesian) and the (fake...err..) imaginary…

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