it seems to be possible but it feels wrong smh

>>8593305
I believe this:
[math]sqrt(ab) = sqrt(a)*sqrt(b)[/math]
Is only valid when both a and b are non-negative.

but is it the same in complex ?
like, everything valid in IR is also valid in C wich means sqrt(ab)=sqrt(a)×sqrt(b) when they're both positive numbers, but the sqrt(-1)=i which leads to i^2=-1 is what makes the complex a new set of numbers, and therefor, it uses the old propreties of N,Z,D,Q and R and like each one of the sets, adds new propreties for itself... so idk if this is legit and correct, or breaking any rule...

[math]\sqrt x[/math] exists if and only if [math]x \,\geqslant\, 0[/math] except if your name is Pajeet.

>>8593425
sqrt(-1*-3) = sqrt(-1) * sqrt(-3) isn't valid in IR though.

>>8593432
even in the set C ?

Obviously the square root can be either positive or negative. Is a troll thread.

>>8593448
>this
How many of you remember discovering this yourselves in like 8th grade? I showed my teacher and she was completely stumped, after that I realized that the only reason they teach complex numbers in high school is so that they can say the word "complex" in a math related context.

>>8593446
In the set c, numbers have the form a+bi.
In your work, it is assumed b=0

You can take the sqrt of a complex number of the form a+bi. It involves some trickery but ends up looking strange

>>8593305
Every = sign on line 2 and after should really be in quotes.

[eqn]
(e^r \cis\theta)^n \equiv e^{nr} \cis(n \theta)
\not \Rightarrow
(e^a \cis\alpha \cdot e^b \cis\beta)^n \equiv e^{na} \cis(n \alpha) \cdot e^{nb} \cis(n \beta)
[/eqn]
Can anyone prove this elegantly?

>>8593432
Poo in the streets, bad math in the sheets.

i^2 = 1 ............

>>8593530
You remember the 8th grade?

>>8593565
you don't? My memory solidified starting about a year before kindergarten started, before that its just short flashes and images.

ITT: What are branch cuts

>>8593448
squrt function is defined to only be positive

>>8593544
i'm sorry the australian education system failed you as it did me.
Ready for a bombshell?

cis(theta) = e^(i*theta)

the proof is almost implicit from there

>>8593550
ehhhh
you mean i^4