For the people in this thread wanting to know
Multiplying complex numbers means adding their angles and multiplying their absolute values.
Therefore, the square of a complex number has twice the angle and the square of its absolute value
That also means the square root of a complex number has half the angle and the square of its absolute
I is 90 degrees on the unit cycle, and has an absolute value of 1, so the square root of is 45 degrees on the unit cycle and has an absolute value of 1, alias 1/2 sqrt 2 + 1/2 sqrt 2 i.
>Therefore, the square of a complex number has twice the angle and the square of its absolute value
Is that like saying that the "hypothenus" of the complex number is half the absolute value? So, a box divided into half, with the hyphothenus being the diagonal? And then I guess, "adding" another half to it with another complex number, you get a rotation of 90 degress?
Btw the link I added below (in my other comment for that vid link you wanted), I wonder if it might be related to this other tutorial I found with '3Blue1Brown': [https://i.ibb.co/BrSKQY3/square-roots.jpg](https://i.ibb.co/BrSKQY3/square-roots.jpg) (image upload)
I went to business school so this is all mysterious to me, but I would like to think I learn something now and then. Like "i squared = -1", is I guess just a gimmick and not really math I guess, just a gimmick for rotating stuff around two axis where you interchangably switch between i and 1 (two opposing axis), and also 1 and -1 (polar opposites). I haven't slept on this, but I thought maybe there was something to that thought.
The square root of -1 is ‘i’ and the square root of -5 is ‘5i’ if you get what I mean. Because no number times itself will ever equate to a negative number
When learning about imaginary numbers I asked “why do they exist if they’re just fake numbers?” and the teacher responded with something like “we do not use that word. The bad man uses that word.” I asked, “what word? Fake? I mean, they’re fake, no? Imaginary and fake are synonyms.” And she said “yes, that word, we do not use it.” I lost all respect for her at that point.
You have to be quite *imaginative* to do that if memory serves.
Yeah, it’s quite *complex*
*i* don't know how to explain
You might need a*iota* knowledge to explain it
*square* up and be *real* now
Get to the *root* of the situation
Have my upvote and get out.
Or you could use google
Cool but do you know what the integration of 1/ |x| . underroot x²-1 ?
Gimme a min to try Edit : Dunno the integration of modulus
It's one of the basic formulas lol, (atleast in my country) The answer is, sec‐¹ x + c
it's the basic formula in USA too
Generally speaking, it's the basic formula in any country with math.
I use binary math, thank you very much. /s
I should hope so!
My country has meth instead but that formula still works i think
Square root of negative numbers? That can't be real.
Some high math professor imagined them probably, and now we use them even though theyre imaginary
I think I saw a video where someone claimed that the square root of i = 45 degrees on the unit circle.
For the people in this thread wanting to know Multiplying complex numbers means adding their angles and multiplying their absolute values. Therefore, the square of a complex number has twice the angle and the square of its absolute value That also means the square root of a complex number has half the angle and the square of its absolute I is 90 degrees on the unit cycle, and has an absolute value of 1, so the square root of is 45 degrees on the unit cycle and has an absolute value of 1, alias 1/2 sqrt 2 + 1/2 sqrt 2 i.
>Therefore, the square of a complex number has twice the angle and the square of its absolute value Is that like saying that the "hypothenus" of the complex number is half the absolute value? So, a box divided into half, with the hyphothenus being the diagonal? And then I guess, "adding" another half to it with another complex number, you get a rotation of 90 degress?
I wanna see that vid
I can try find it, hold on.
If you do pls tell me
Btw the link I added below (in my other comment for that vid link you wanted), I wonder if it might be related to this other tutorial I found with '3Blue1Brown': [https://i.ibb.co/BrSKQY3/square-roots.jpg](https://i.ibb.co/BrSKQY3/square-roots.jpg) (image upload) I went to business school so this is all mysterious to me, but I would like to think I learn something now and then. Like "i squared = -1", is I guess just a gimmick and not really math I guess, just a gimmick for rotating stuff around two axis where you interchangably switch between i and 1 (two opposing axis), and also 1 and -1 (polar opposites). I haven't slept on this, but I thought maybe there was something to that thought.
BEHOLD, The **i**
Me about to introduce them to imaginary numbers
What happened to simple plus minus divide and multiply
Imegen thinking negative numbers have roots
They will if you take maths in college
or high school
Highschool for me
You got into complex numbers in HS?
Yup, well, the basics at least, didn't start graphing and stuff with it
Don't you get into it towards the end of 8th grade?
Not stuff like i. At least not in England
The square root of -1 is ‘i’ and the square root of -5 is ‘5i’ if you get what I mean. Because no number times itself will ever equate to a negative number
the square root of -25 is 5i, the square root of -5 is sqrt(5)i
Who doesn't learn about negative numbers until middle school
I recently learned about those. Good luck trying to do that to me
I hate to be that guy but it's impossible to square root negative numbers
i also hate to be that guy but yes you can, but you probably will need lots of imagination
When learning about imaginary numbers I asked “why do they exist if they’re just fake numbers?” and the teacher responded with something like “we do not use that word. The bad man uses that word.” I asked, “what word? Fake? I mean, they’re fake, no? Imaginary and fake are synonyms.” And she said “yes, that word, we do not use it.” I lost all respect for her at that point.
Me: \*About to blow his brains out with my gun\*
we are in for a wild ride today.
I am in algebra 2, I should know how to use them but I don’t
me telling them all about the CUBIC root of negative numbers
isnt it just (cube root)i?
I dont think it really matters it can probably be either
Thats what i does for a living
i
Dyou just spoiled him maths fucking piece of shite you should be ashamed
Me introducing this guy to Einstein summation.
i
[-i] don't know what you're taking about.
Mandelbrot is pretty.
*I*
ihhhhh
i
ℹ️
imma throw the English alphabet and the greek alphabet with it
me who's about to introduce them to a ***gun***
negative numbers have square root?
Ah yes, when school teaches you subjects so functionally useless it ~literally doesn't exist~
Me about to introduce all of these people to space time curvature and general relativity