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1/13/2014 3:41:37 AM
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Plus or minus. It's just an easier way to say +2 and -2. Like if you have an equation x^2 - 4, you can factor that into (x+2)(x-2). The zeros of the equation are at +2 and -2, but you can just say x = ±2.
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  • Right, so if "x" were an imaginary number for the equation x² = -9, I could answer x = ±3 because -3 × 3 = -9

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  • If we are talking imaginary numbers, the answer would be that x = ±3i

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  • Edited by DarkSpyda04: 1/13/2014 4:36:07 AM
    I don't even understand the whole ±3 versus ±3i bit. It's all -blam!-ing bullshit as far as I'm concerned and should all equal out to the same result. Why in batty hell is ±3i the right answer when ±3 isn't?

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  • Because 3i is an imaginary number while 3 isn't.

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  • So are you telling me that it's -3i × 3i = -9?

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  • No, because that wouldn't be squaring. -3i x 3i = 9, since i^2 = -1 and 3 * -3 = -9. (3i)^2 and (-3i)^2, however, both equal -9. i^2 = -1 and both 3^2 and -3^2 equal 9.

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  • Edited by DarkSpyda04: 1/13/2014 5:02:32 AM
    [quote](3i)^2 and (-3i)^2[/quote] You mean (3i)^2 and (-3)^2 = -9. Wait no because -3 × -3 = +9. I see what you did there.

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  • Edited by Kamots: 1/13/2014 5:04:10 AM
    No. -3^2 is -3 * -3, which equals 9. Negative * Negative = Positive. Edit: Yeah.

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  • Edited by DarkSpyda04: 1/13/2014 5:13:33 AM
    Okay, so how do we do the math in x^2 = -9? (-3 * -1)(3 * -1) = -9 as in (-3i)(3i) seeing as x = ±3i?

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  • Not quite. Remember that squaring is involved. Both terms need to be the same to equal -9. And that i = sqr(-1).

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  • Edited by DarkSpyda04: 1/13/2014 5:34:22 AM
    [quote]Both terms need to be the same to equal -9.[/quote]It's impossible to get (-9) if both terms are the same! Do you mean that 3i × 3i = -9 because 3 × 3 = 9 and i × i = -1?

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  • Edited by Kamots: 1/13/2014 5:35:50 AM
    Nope. Take it this way: (4*3)^2=144. (4^2)(3^2)=144. 4^2=16. 3^2=9. 16*9=144. Therefore, (3*i)^2 = (3i)(3i) = (3^2)( i^2). i=sqr(-1). i^2=-1. 3^2=9. (3^2)(i^2) = (9)(-1) = -9. The same applies for -3.

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  • Alright, I think I get it now. Any real number [b]times itself [/b]gives a positive result, including a negative times a negative. For this reason, we are blessed with imaginary numbers as they have the strange effect that I × I or I^2 = -1. If this is the case, the square root of -1 is "I". This is the basic foundation of imaginary numbers. With the magic of imaginary numbers, (3i)^2 = -9 just as I^2 = -1

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  • Edited by DarkSpyda04: 1/17/2014 9:36:43 AM
    Yeah... I'm gonna have a real hard time with imaginary numbers in the future. *Goes off to play Streets of Rage* *Plays game and rages*

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