Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
mentu960
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Joined: Sun Sep 26, 2010 4:17 pm
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It all started in my pre-calc class when my teacher gave us a packet and he had us circle an answer to a question. I'm going to save you guys some time and just say that I came up with a situation in which he couldn't give me an answer. So I figured this would be my next best option, so I really encourage you all to help find out why there are two answers to this question...

the link leads to my facebook picture... it is to difficult to type out so that is the easiest way to view it... so if someone or a multitude of people can individually or collectively come up with a way to explain this problem that would be greatly appreciated.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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Nothing displays. Sorry.

Thank you!

mentu960
Posts: 2
Joined: Sun Sep 26, 2010 4:17 pm
Contact:

Re: Why are there two answers???

sqrt(-3)^2 = sqrt(9) = 3

AND

sprt(-3)^2 = (sqrt(-3))^2 = (i (sqrt(3)))^2 = i^2 (sqrt(3)^2) = -1 (3) = -3

P.S. thank you for that article, I have been curious about the most efficient way to type mathematical terms for a long time B)

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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sqrt(-3)^2 = sqrt(9) = 3
If you mean $\sqrt{(-3)^2}$, then you are taking the square root of 9. If, on the other hand, you mean $\left(\sqrt{-3}\right)^2$, then you need to change to complex values:

. . . . .$\left(\sqrt{-3}\right)^2\, =\, \left(\sqrt{3}i\right)^2\, =\, 3(-1)\, =\, -3$

As soon as you start dealing with negatives inside square roots (or any even-index root), you have to convert to complex numbers. You gain the ability to deal with negatives inside radicals; you lose the ability to switch around between powers and radicals (so you cannot move the squaring inside and outside and back again).