If r is a positive number and -r is a negative number. Is it true that 1/(√-r) = (√1/-r)?
I'm thinking, no it's not true, because if r=3, -1/(√3) does not = 1/√3. However 1/(√-3) = -1/√3.
But, I wouldn't know how to explain it. (btw. Is my example sufficient enough?)
Any help is appreciated. Thanks guys.
Update:Yeah it's can be troubling when mistyping the problem.
Anyhow, I figured out the solution with a tutor.
Thanks for all of your help!
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False, 1/√(-r) = 1/(i√r)... Make notes that i = √-1.
Good luck!
I almost passed on this. I detest questions with crappy use of parenthesis. They leave the real question ambiguous.
for any real number x; 1/âx = â(1/x)
if your question is: Is it true that 1/(â(-r)) = â(1/(-r)) then I've already answered it.
if your question is: Is it true that 1/(â(-r)) = (â1)/(-r) then obviously it is false.
â(-1) = i and i² = -1. i is NOT a real number.
for positive r; 1/(â(-r)) = 1/(â(i²*r)) = 1/(i(âr))
multiplying both top and bottom by i (because the convention is not to leave i in denominators if possible)
1/(iâr) = i/(i²âr) = i/(-1âr) = -i/âr
and of course usually you remove radicals from the denominator, too (by convention)
-i/âr = -iâr/(ârâr) = -(iâr)/r
BTW 1/ (â-3) IS NOT -1/â3 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !
Wait a sec.
1/sqrt(-3) = 1 / (sqrt(3) i)
That doesn't equal -1 / sqrt(3).
Let r = 4
1/sqrt(-4) = 1/2i
sqrt(1/-4) = sqrt(1/2i)
So your first statement is true, but not for the reason you say it is, which is false.
are u square rooting a negative number ? hope not ... otherwise I can't understand what u'r asking :(