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Old April 15th, 2012, 01:38 AM   #11
Hijikata
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Default Re: -1 = 1

25 has two roots, one negative and one positive. Taking the root of -25 has only one result, the imaginary root (5i).

Also, yes, the answer is 288. I actually made a mistake writing it down--the troll logic order is 48/2 (9+3), intentionally ambiguous to fool the reader into thinking the answer is 2 instead. (48/24 = 2)

edit: Because the value of i shifts every odd exponent.
Code:
i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i
i^4 = -1
If you have i * i, that's not the same thing as (-1 * -1)^1/2, because exponents aren't distributive. You have to add the exponents or leave the bases separate until you resolve the exponent.
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Last edited by Hijikata; April 15th, 2012 at 01:45 AM.
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Old April 15th, 2012, 01:57 AM   #12
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Default Re: -1 = 1

Quote:
Originally Posted by Hijikata View Post
If you have i * i, that's not the same thing as (-1 * -1)^1/2, because exponents aren't distributive. You have to add the exponents or leave the bases separate until you resolve the exponent.
One of the properties of exponents I'm guessing. So that you can avoid situations such as this.
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Old April 15th, 2012, 03:22 AM   #13
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Default Re: -1 = 1

I mean, look at it this way:
Code:
2^2 * 2^2 = 2^4 = 16
This is a common base (2), with a common power (2). You multiply them together, and receive an increased multiplier but no change in the base.

If you were to keep the exponent fixed, you would be able to multiply the bases in the above example, but you'd be wrong if you changed the numbers:
Code:
3^3 * 3^3 = 3^6 = 81
3^3 * 3^3 = (3 * 3)^3 = 729
The proper way to handle exponent multiplication is to leave the bases the same and add the exponents. In the faulty line in the OP, you fall into the trap of the above example by keeping the exponent fixed and multiplying the bases.
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Old April 15th, 2012, 03:59 AM   #14
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Default Re: -1 = 1

If you ponder equations rather than sleep walk while laboring you will wind up a crazy janitor. They were once like us, but they chose to drive their selves mad by attempting equations.
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Old April 15th, 2012, 11:08 AM   #15
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Default Re: -1 = 1

@Hijikata, that's incorrect. 3^6 = 729. The rule when multiplying exponential #'s is: If the bases are the same, you can add the exponents while keeping the base. If the exponents are the same, you can multiply the bases while keeping the exponent. (But you can't do both if both are the same).

The reason that (-1)^1/2 * (-1)^1/2 = (-1 * -1)^1/2 is incorrect, is that in the rule

Code:
√(a) * √(b) = √(a * b)
,

a and/or b must be a positive, real #.
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Old April 15th, 2012, 04:18 PM   #16
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Default Re: -1 = 1

That's what I get for doing math at 5 in the morning. In this topic, I am told who is the boss.
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Old April 15th, 2012, 07:48 PM   #17
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Default Re: -1 = 1

The key here is in the definition of square root and not ignoring the fact that the square root function yields two results. The square root of a number a is y, such that y*y=a. We sort of mentally ignore one root of the square root function, but there's two. As Hiji mentioned, sqrt(25) is equal to both +5 and -5. Similarly, sqrt(-25)= +5i and -5i.

-1*-1 = 1, and 1*1=1. The important distinction is that sqrt(1) =/= 1. It's a function that has two roots, +1 and -1. Similarly, 1 raised to any power isn't equal to 1. It's the component along the real axis probably has a value of 1, but there's a difference between the point 1+0i and the roots of the equation x=1^a.
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Old April 16th, 2012, 08:37 PM   #18
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Default Re: -1 = 1

Now, let's all find the area under the curve!!11
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Old April 20th, 2012, 11:11 AM   #19
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Default Re: -1 = 1

so it's basically the same as this:
-2
=(-8)^(1/3)
=(-8)^(2/6)
=6√(-8)^2
=6√64=2

(just want to point out that the six before the root, doesn't mean 6 x ..., but instead root to the sixth (i have no idea how you say it in english))
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Old April 20th, 2012, 11:56 AM   #20
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Default Re: -1 = 1

Quote:
Originally Posted by Hellz Lips View Post
which i suck at, which is why im a psych major.
There's more math involved in psychology academics than many, many other fields of study. Understanding and practicing statistical analysis is imperative to obtaining a workable degree in the field.
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