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More ways to get Braingle...

`t` to the 1/8th power

Math brain teasers require computations to solve.

 

Puzzle ID:#187
Fun:** (2.07)
Difficulty:*** (2.5)
Category:Math
Submitted By:trojan5x***
Corrected By:cnmne

 

 

 



How might a mathematician describe a number `t` held to the following condition:
When (t+1) is subtracted from t and the result is raised to the 1/8th power.

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Answer

Imaginary Number.
Whenever (t+1) is subtracted from `t`, you will simply be left with -1. -1 raised to the 1/8th power is the same as taking the positive root of something. When taking the positive root of any negative number, you are left with an imaginary number.

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Comments

Phyllis*
Feb 01, 2001

What is a rooth?
jmanheim
Feb 02, 2001

Your second sentence is syntactically incorrect.
thephirm
Oct 18, 2001

Your claim that taking the positive root of any negative number results in an imaginary number is incorrect. For example, the cube root of -1 is -1 (-1 * -1 * -1 = -1). However the even root of any negative number will be imaginary.
canu*
Jul 13, 2004

The words in the teaser look like English words, but put together they have no meaning in English or in math.
Sane***
Mar 20, 2005

I did the subtraction wrong and came out with:

1/100 000 000
0.00000001

darthforman*
May 25, 2005

stephiesd**
Dec 09, 2005

i read it wrond after i did the subtraction, i read it as the -8th power, resulting in -1.

anyhow, we haven't covered imaginary numbers yet. i think they're next chapter.
mr_brainiac*
Jan 11, 2006

I don't think that the answer is really an imaginary number, I think it's more likely an imaginary imaginary number, or maybe it's an imaginary imaginary imaginary number, or maybe it's ...
lessthanjake789*us*
Jan 29, 2006

wrong... all of you. the number t is a positive, real number. let t = 100, t+1 = 101. t-(t+1) = -1, raised to the 1/8th is, truly an imaginary number, but as you can see, "t" is ANY real number, positive or negative. sorry, but poorly thought out teaser
MethlosAgb*
Mar 12, 2006

I thing i might put my head under a pillow for a while
Brainy_1Aus*
Mar 18, 2006

That hurt my head! Nice job though!
MadDog72**
Mar 23, 2006

I see four problems with this teaser:
1) It asks for the number t, not the value of (t-(t+1))^(1/.
2) Why bother with t? Isn't it obvious that if t+1 is subtracted from t, the result is -1?
3) The answer is vague. I actually computed the answer, only to find that all you wanted was 'imaginary'.
4) It's not an imaginary number! An imaginary number is a number of the form b*i, where i^2=-1. The answer is of the form a + b*i, where a is nonzero (there are actually 8 answers, but they are all of this form). The answer is complex and not real, but not imaginary either.
Krystle*us*
Jul 23, 2006

wow, i'm not good at math at all
QrystalAca*
Jul 29, 2006

I figured that a mathematician would call 't' TRIVIAL. After all, it got subtracted out of the situation right away.

There must be a way this teaser could be improved so that it asks what it means to ask... although of course MadDog72 is absolutely correct in stating that [-1]^[1/8] is technically considered complex, not imaginary.

Does anyone care that [-1]^[1/8] has 8 answers?
Let A = cos(pi/. Let B = sin(pi/.
Then [-1]^[1/8] =
( A + B*i, B + A*i, -B + A*i, -A + B*i,
-A - B*i, -B - A*i, B - A*i, A - B*i )
Anyways, I don't care if anyone else doesn't care; I wrote it because I care. So there.
QrystalAca*
Jul 29, 2006

eeek my answer got invaded by sunglass dudes!

That should say:
Let A = cos[pi/8]. Let B = sin[pi/8].
dimez_00**
Oct 22, 2006

i figured this:

(t+1)-t=? ?^1/8 therefore i got

t+1-t=1 1^1/8=the 8th root of 1 which is 1
ChristheGreat*us*
Nov 12, 2006

Hmm.. you did't include the fact that pi to the 3rd power minus the radius of a duck's butt plus the deepness of a toilet = 5 times the 3rd trigonometric function plus the amount of time it takes for the final star to impact the earth causing free cake for everyone!
EA_KLEINAil*
Mar 15, 2007

whoever wrote this has some loose marbles in his keppie
jamesbondAsg*
Apr 19, 2007

ya ryt
SRB_1807Ain*
Aug 17, 2011

I love 2 eat ducks..



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