Minus One
posted by ToM at
1:10 PM
Saturday, June 20, 2009
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21 Comments:
the answer is 1i... use this website(s) for help:http://www.factmonster.com/ipka/A0875883.html;http://www.conservapedia.com/Square_root. any time u have a negative in a square root radical, find the absolute value of the square root and put a cursive i after the answer. This is what my math teacher told my class. Isn't this a homework question?
i
The "i" is used to represent the square root of a negative number in mathematics. This come in handy when studying electrical engineering among other things. Keep up the good questions you'll go far in life with a curious mind :D
most of us know the squere root of "-1"is (I) "abbrive to the word imiginagry number" so let see this puzzl in different view
I will now prove the root of -1 is 1 but I make a mistake find it
let -1=-1
squere the two sides
1=(-1)^2
then make root
then 1=-1
then take root to the to sides
so the root of -1 equal 1
Kindman
Thats not quite how it works
-1=-1
if you square both sides you get
+1=+1
then take the root of each side you get
+1=+1
there is no proof to saying that i=1 because its not true. 1 is a real, whole, rational number where i is an imaginary number. They are two completely different things.
i agree with kindman actually...though noone wud actually approve of it btw anon above me,
-1 = -1 (got thru obvious fact)
-1^2 = -1^2 (^2 it )
so 1 = -1^2 (as -1^2 is = 1... leavin the second part of the equation alone)
sq. rootin both sides we get 1 = -1
this is something like tht thin where 1 = 2 is proved by unusual methods also like tht one like 0/0 can b 1 (a/a =1) r it can b infinity (anythin by 0)
But v havnt started imaginary nos in school, so i dunno very well im jus sayin frm my experience in 9 an 10.
PS: i noe abt it a bit like i noe the meanin of i and how to get it an stuff..)
First let me say the guy above me has horrible grammar he/she should hope his/her English teacher doesn't read :D
Second the a/a=1 rule, when spelled out completely says when a does not equal zero. As far as a/0=infinity is not true entirely. If you have a/b and b approaches 0 then a/b approaches infinity (try graphing this on a Cartesian plane) however if b=0 strictly speaking the result is undefined.
Lastly with the above proofs saying that 1=-1 are, in a manner of speaking, correct, however common sense says that owing a dollar is not the same thing as having a dollar. Not to mention most people forget that when taking the square root of a number there are two answers because squaring a negative number results in a positive number. i.e. sqrt(81)= 9 and -9 because -9X-9=81 and 9X9=81
On the other hand saying that
-9=-9 => (-9=-9)^2 => 81=(-9)^2 => sqrt(81=(-9)^2) => 9=-9
is not a correct statement even though the rules of math seem to have been followed here. I'm not 100% sure how to prove this is mathematically wrong but commons sense, if you have any, will tell you this is wrong.
Someone must have just found out about 'i' in their high school algebra class and thought it was the most amazing thing. Basically it's a way to assist in the calculations of the square root of a negative number.
What happened to the "No Homework Questions" rule?
1i
it is a complex no
1i
it is a complex no
1i
it is a complex no
1i
it is a complex no
Seriously guys... basic maths...
1 does not equal -1
REMEMBER when you square root a number you have TWO answers... one positive AND one negative. If you don't believe me, I'll show you by an example:
x = (square root of)25
x^2 = 25
(square both sides to get rid of the square root)
NOW you ask yourself, what can 'x' possibly be!? Oh 5 obviously, you say to yourself... cause 5 times 5 is 25. BUT hopefully you can also deduce that -5 times -5 is also 25! (OMG I know, that's amazing!). Therefore 'x' can have two answers, -5 and 5.
This happens for every number(I think). SO that means:
1 = -1^2
(squareroot)1 = (squareroot)-1^2
(+ or -)1 = (+ or -)1
Gah... this would be so much better if I had a plus/minus symbol T.T.
Anyway, like the people above me explained... square root of '-1' is called an 'imaginary number.' But it actual fact, 'imaginary number' is not imaginary at all lol. Its part of complex numbers.
Off the subject slightly, but does one imaginary number equal a different imaginary number?
Does an imaginary duck equal an imaginary dog?
Maybe, they look the same, weight the same, bark the same, right?
I disregard your reality where an imaginary duck equals an imaginary dog, and substitute it with my own in which an imaginary duck equals an imaginary platypus and ONLY an imaginary platypus!
I don't think an imaginary duck equals an imaginary platypus.
Although they do appear equal, I am not sure they are the same beyond 3 significant figures.
Draw a square with an area of -1.
Then the length of one side of it is the square root of -1.
i
OK! heres what i think. Since its happening like this i have always been taught that if this happens you put 1+-. The plus and minus are supposed to be the plus on top and minus on bottom.
i agree with the 6th comment!
You can't say there is ONE square root of -1.
The square root of a positive real x is defined as THE positive number which square is x.
But you cannot say i is positive "because there is no negative sign", -x is positive if x is negative.
Note that i=-1/i.
So you could say i AND -i have both -1 as square, but that doesn't mean one of them is THE square root of -1.
Karys
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