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Cervantes

Thu Nov 03, 2005 2:18 pm


i = non-i and an exponent question

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A few weeks ago I thought this up:

http://www.imagesharing.com/files/imaginary_number_problemv70c.JPG

What's the problem?

One of my friends tried to explain it using BEDMAS.  Brackets before exponents.  I forget now just where he said the problem was, but I retort to him by saying that brackets are not needed.  Expressions can also be written in this format, which does not contain any brackets:
http://www.imagesharing.com/files/exponentsl8mh.JPG
What is the value of the above expression?  Is it 3^(3^3) = 3^27?  Or is it (3^3)^3 = 27^3 = 3^9.  (Multiplying exponents.)

In other words, do you work from left to right & bottom to top or right to left & top to bottom?


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Boo-chan

Thu Nov 03, 2005 2:45 pm



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ok, (-x)^.5=(-1)^.5 *x^.5=x^.5(i) for x>=0

Your statement is true for x=0

Your statement is true for x 0, and an expression on the right which is a real number when x > 0.  (When x < 0, the left side is real and the right side is imaginary.)

What you've got in words up there is pretty much the next two equations in my little line.  I know the left side doesn't equal the right side, but I've used the exponent laws to, seemingly, make them equal.

Back to the drawing board!

Here's the reason I was wondering about the order of operations of the exponents.  It's essentially just an expansion of the first step.
(-x)^.5 = (-x)^(2*.25) = (-x)^2^.25

By the exponent laws, this should be valid, since an exponent raised to another exponent multiplies the exponents together.  And no brackets are needed in the right side of this equation.  Or are they?


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Naveg

Thu Nov 03, 2005 6:32 pm



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The laws of exponents do not apply to imaginary numbers. (-x)^2^.25 cannot be solved correctly using exponent laws since, if it is, the resulting value is imaginary.

In fact, I'm pretty sure the laws of exponents do not always work for negative real bases, or fractional/irrational exponents at all. I may be wrong though.


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Boo-chan

Thu Nov 03, 2005 7:56 pm



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Yes, I did mean to put a * in there.... I'm only good at math when I write it down on paper.

But I don't see the other problem. If x>0 then (-x)0 then (-x)