awn786
What is the square root of minus 1.
When i do it in a scientific calculator, it says 'i' (imaginary unit) and i have no idea what that means
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awn786
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\[\sqrt{-1} = x \] what is the value of x
awn786
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please dont put links
zaynahf
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Imaginary numbers result when you are taking the square root of any negative number:
For an example, \[\sqrt{-1}\] = i
\[\sqrt{-25} = 5i\]
The 'i' is kind of like the negative sign
awn786
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so what is an imaginary unit
zaynahf
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I know of a video you can watch if you want to
awn786
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yes what is the vid @zaynahf
hba
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did you see the link @awn786
It has everything.
awn786
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yes i did but what is an imaganary unit
awn786
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WOW OMG complicated @hba
zaynahf
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The first link is really straight forward, try that
hba
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@awn786 Well,I tried to simplify and put everything :)
awn786
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thanks for trying. @hba
hba
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You are welcome :)
awn786
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listen and can u give a simple i word answer: \[\sqrt{-1}=x\] what is the value of x in numbers.
awn786
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1 word answer*
awn786
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not i word
hba
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I can help you understand what imaginary numbers are.
So,the base of imaginary numbers is actually laid upon some of the things like
\[\huge \ i=\sqrt{-1}\]
The other thing is
\[\huge\ \omega=\frac{ -1+i \sqrt{3} }{ 2 }\]
awn786
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whats w
hba
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We call this omega,It's derivations is given in my link :)
awn786
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whats w @hba
hba
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Now as per your question.
x=root{-1}
x=i
Here i is actually iota and it is an imaginary number.
hba
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That's omega @awn786
awn786
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whats omega
hba
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@awn786 Please check the link i have provided.
It has everything
Please give it a read.
awn786
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i said in numbers. your answer is basicly my question
hba
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Well,In numbers it is sqrt{-1}
awn786
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it should be easy shouldent it.
awn786
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i dont understand ur link
awn786
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what is omega
hba
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I have already told you what omega is.
awn786
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no u havent @hba
hba
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I said it is -1+i sqrt{3}/2
awn786
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ok (i dont get it but ok) i' only in year 9 doing my gcse's
GCR92
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\[\sqrt{-1}\] doesn't exist as a the REAL number you are asking for, because there's no number that you can square (because of the SQUARE root) and gives you -1
GCR92
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you just need to know what a square root is
awn786
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i know what a square root is ofc
GCR92
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that's why there's no sqrt of ANY negative numbers, because everthing squared is BIGGER than 0
GCR92
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(possitive)
awn786
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oh i get it so its an imaganary number because it cant exist?
awn786
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you have the best responce
GCR92
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EXACTLY, it CAN'T EXIST as a "normal number"
awn786
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thank u so much.
awn786
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^^^^^^ @GCR92
GCR92
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so mathematicians around XVII century had to figure out another type of numbers, called COMPLEX numbers, and the first number of complex numbers is \[\sqrt{-1}\]
GCR92
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they INVENTED it
GCR92
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you are welcome
awn786
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ur a genius @GCR92
GCR92
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not really, but thanks!
GCR92
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ill draw you something
awn786
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you can bring the most complex thing and make others understand. are u sure ur not related to prfsr.
brian cox
GCR92
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|dw:1358026644045:dw|
GCR92
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hahaha you amuse me, nothing is hard when you have an amazing teacher, and I have it right now.
GCR92
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you understand what I drew?
awn786
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yeah u drew a number line. who is ur teacher
GCR92
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My uncle, who's been teaching maths since he was 15 and he's now 57, anyway, let's go back to our imagination
awn786
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|dw:1358026974868:dw|
GCR92
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ALMOST
awn786
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|dw:1358027044754:dw|
awn786
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|dw:1358027175723:dw|
GCR92
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|dw:1358027034198:dw|
GCR92
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you put the axis pararell and it's perpendicular cutting in 0
awn786
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|dw:1358027255837:dw|
GCR92
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that's why i said almost, because you figured out ANOTHER line, and that would make a 300 year old mathematician proud
awn786
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yepeee
GCR92
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because they CAN be negative in their new axis, the imaginary axis
GCR92
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the imaginary line
GCR92
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it is not allowed to be a negative square root in the REAL line, but it is in the imaginary one
awn786
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so in imaginative can they ever be 3i or always do they have to be -3i
GCR92
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so we just call it i, like we call 1 one
GCR92
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there are imaginary postive numbers and imaginary negative numbers, under 0
GCR92
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real negatives are at the left of 0, so why can't there be negative imaginary ones?
awn786
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|dw:1358027454145:dw|
awn786
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above 0 is positive?
GCR92
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if you delete the minus inside of the root, it would be a real number then!
GCR92
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Yes that's what i was writting
GCR92
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and under 0 negative, i forgot to draw it
GCR92
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just like the real line but perpendicular
GCR92
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above 0 goes posstive until inifinity and under 0 negative until infinity
awn786
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and on the real line is it same?
GCR92
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|dw:1358027632303:dw|
GCR92
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they are two separated lines.
awn786
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bye i need to go. if i see u tommorw here i will carry on the conversation.
GCR92
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okay, sure! bye! you are smart btw, you figured the other line very well.
GCR92
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figured out*
awn786
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thanks
awn786
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@GCR92 im back
Krishnadas
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complex numbers
AravindG
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i is actually an imaginary number used to give value to \[\sqrt{-1}\]
awn786
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yes i get that.
awn786
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Look above^
ParthKohli
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Wait, no!
awn786
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what?
ParthKohli
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\(i\) is defined as the imaginary number such that \(i^2 = -1\), not \(i=
\sqrt{-1}\).
awn786
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no ur wrong
awn786
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wait
ParthKohli
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How so...?
awn786
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watch
awn786
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wait
awn786
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and also its just common knowlige
awn786
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Knowledge*
ParthKohli
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Yes, \(i\) is one of the square roots of \(-1\). But \(i \ne \sqrt{-1}\).
ParthKohli
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I mean, \(\sqrt{-1} =i,-i\)
ParthKohli
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So you must define \(i^2 = -1\) if you don't want things to mess up
awn786
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wow gcr92 was WAY better at explaining things
ParthKohli
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What would you like to learn?
awn786
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apparantly his teacher is hgis uncle who started teaching him maths when he was 15 an now is 50
awn786
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wait
awn786
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carry on from:
awn786
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|dw:1358591619083:dw|
awn786
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look above^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
ParthKohli
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Re and Co, yes.
awn786
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ermmm it needs to be simple
awn786
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nope its not
awn786
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sorry
awn786
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where is GCR92
GCR92
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Here. What's up?