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R. Brown
Posts:
54
From:
texas
Registered:
12/29/05
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Imaginary Plane Problem
Posted:
Mar 13, 2007 3:35 PM
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consider the following:
2 - 1.4142135i.........represents a complex number.
then, could not the graph point on the imaginary plane be stated as:
x= 2........(where: x= axis of reals)
i= -1.4142135..........(where: i=axis of imaginaries)
At this point, if you 'agree' that what I have just stated is reasonable and coincides with standard geometry, consider this:
Wouldn't it make 'more' mathematical sense to have stated the coordinates as:
x= 2..........(where: x= axis of reals)
z/i= -1.4142135..........(where: z/i=axis of imaginaries)
Now I will illustrate why:
z/i = -1.4142135.....eq.101
Let's multiply both sides of eq. 101 by i:
i * z/i = -1.4142135 * i
z= -1.4142135i .....
We have No problem transferring the (i) to the RHS of the equation!
Now let's look at the standard statement:
i= -1.4142135......eq.201
If we now multiply both sides of eq.201 by i, what happens?
i * i= -1.4142135 * i......eq.201-a
i2= -1.4142135i.. is this true?
this becomes:
-1 =/= -1.4142135i
NO! The equation above is obviously not true!
Therefore the idea of graphing 'imaginaries' on an (x & i axes system) makes LESS sense than graphing
them on an (x & z/i axes system)!
#Puzzles and Ideas compliments of Col. Rbtx, the Barnyard physicist of Texas
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