Experimental test to train myself before getting into high school
This is the easiest question btw
(Update): turns out I was overthinking because of sleep deprivation haha, it’s solved now
#What does “i” mean
plush junco
rustic pondBOT
half nebula
the famous imaginary constant defined by $i^2 = -1$
valid abyssBOT
clôud
left dagger
the famous imaginary constant defined by $i^2 = -1$
The encircled problem doesn't seem to mention it anywhere tho.
half nebula
i am referring to the calculator output
no idea what the relationship is between the calculator and the problem
left dagger
Aah
distant obsidian
Experimental test to train myself before getting into high school
This is the ea...
Okay, so just looking at your calculator input
Not the problem
but every cubic function has 3 roots, this is a result of a theorem
unnecessary to know why
but these roots aren’t always real
a real number is just our basic number line
plush junco
What the fu
plush junco
1, or -1, or 10000
Got it thanks 
distant obsidian
well you can ask the question then, if the square root of 4 is 2
what’s the square root of -4 ?
plush junco
what’s the square root of -4 ?
There isn’t?
distant obsidian
it can’t be 2 as 2•2=4≠-2
there is!
it exists in something called the complex plane
these are also called imaginary numbers
it’s described such that
$\sqrt{-1}=i,,i^2=-1$
valid abyssBOT
OK32
distant obsidian
these numbers help us work with cases such as this
roots of a negative number
mathematicians for centuries simply ignored them, treated them as fake
BUT
they do exist and are actually incredibly useful in computations
famously very useful in shrodinger’s wave function
but so that is all your calculator is telling you
4i is nothing but
$4i=4\sqrt{-1}=\sqrt{-16}$
valid abyssBOT
OK32
plush junco
distant obsidian
don’t be scared of them
just a simple mathematical trick
to give us a way to work with something that our number system didn’t let us
think of it more as just something that wasn’t planned for
so we had to find a way around it without starting anew
plush junco
Got it
distant obsidian
Goodluck with your learning!
distant obsidian
Great job!
plush junco
Did a redo 15 minutes later
Now it’s correct
Thank you for blessing me with your knowledge @distant obsidian
Wait a damn second
BLYAT
plush junco
Experimental test to train myself before getting into high school
This is the ea...
This is solved now
Rookie mistake
languid saddle
This is solved now
good
if you are done with the thread and do not have any other query, you can close it by typing .close or .solved 
plush junco
.solved