complex number be getting too complex

[dusk bane]

where did I go wrong and what is the right answer to this?

[dawn sinew]

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2. Once someone helps you, say thank you and close the thread with:

+close

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[pastel mirage]

the second part is wrong

and the top part is right

let me explain why

[dusk bane]

yes please

[pastel mirage]

here is the mistake

[ashen relic]

wolfqz

[pastel mirage]

the thing is the you cannot split the root like that when dealing with negatives inside the root

you have to be very careful

[dusk bane]

is that a convention or is there a reason ?

[pastel mirage]

as the above result literally breaks math

[pastel mirage]

convention iirc

[dusk bane]

it does lmao

[pastel mirage]

but its intuitive

[dusk bane]

how is it intuitive?

[cold sorrel]

no your step to is wrong

wait sorry

[dusk bane]

feel free to judge critically as it will help me in remembering this mistake

[cold sorrel]

wait i texted a similar exp for one more q

[pastel mirage]

1 is sqrt((-1)(-1)) but not sqrt(-1) times sqrt(-1)

[pastel mirage]

oh okay

[cold sorrel]

let me get it

looks like it was closed

suppose i have a number 4
so now i am asked to find root 4
i will use this idea
rootof 4=root of 22
so i can say root 2 root2 =root 4
so then i say 2=root 4
but now lets try another way
root 4=root -2-2
root -2root -2 should be equal to root of 4
so lets do it

[pastel mirage]

i already showed this but with 1

[cold sorrel]

so i get root2 * root 2 i^2=root 4
it becomes root 4i^2=root 4
and we get -root 4 =root 4
which makes no sense
as rhs = equal to lhs

oof sorry

so we cant split with negative

[dusk bane]

aah but root-2.root-2 gave us -4

[pastel mirage]

it did NOT

[cold sorrel]

no it gave - root 4

[pastel mirage]

yeah

you edited that lmao

[cold sorrel]

still it is root

[pastel mirage]

what

[dusk bane]

I see so basically we can't go on splitting numbers into negatives while they are under roots

[cold sorrel]

• root 4

[cold sorrel]

yeah

[pastel mirage]

yeah

[dusk bane]

yes made an error

[cold sorrel]

hm the point came out of no where

[pastel mirage]

- root 4

it adds a point

• abc

[cold sorrel]

oh

[pastel mirage]

the hyphen

[cold sorrel]

dman

[pastel mirage]

if you dont add a space it doesnt

[cold sorrel]

damn

[pastel mirage]

lmao

[cold sorrel]

asterisk does italics

btw bot is up and working nice work

[dusk bane]

is it like

9=9

sq.root both sides

3=-3

[pastel mirage]

what

bro no

kind of, i guess

but square roots, by convention, output the principal value

[cold sorrel]

yeah you have |a|

[dusk bane]

what do you mean by principal value?

[cold sorrel]

mod

ulus

[pastel mirage]

no

think of it, kind of like the first value

for square roots it acts like a modulus

i wont go into much depth but it may be different for other functions (eg lambert w function)

[dusk bane]

yes

[cold sorrel]

oh ok

my bad

[pastel mirage]

dw about it

[dusk bane]

so basically 9=9 sq rooting both sides gives us mod3=mod3

right?

[cold sorrel]

modulus

[pastel mirage]

yeah

[cold sorrel]

and mod is different

[pastel mirage]

mod represents modulo

but you didnt put an input for it so its okay

[cold sorrel]

yeah that is for remainders

[dusk bane]

what is modulo ?

[cold sorrel]

modulus is represented by |a|

[pastel mirage]

dont worry

[cold sorrel]

its another concept

[dusk bane]

I see

[cold sorrel]

its to do with remainder in the most simplest sense

[pastel mirage]

|3|=|3| spits out 3=3 not 3=-3

[dusk bane]

or -3=-3

right?

[pastel mirage]

NOT

[cold sorrel]

modulus is like magnitude

no sign

its always positive

|-2|=2

[dusk bane]

yes

[cold sorrel]

|3|=3

[dusk bane]

sorry about that

[cold sorrel]

no problem

[dusk bane]

thank you @cold sorrel and @pastel mirage for answering my doubt

[upbeat oar]

@dusk bane has given 1 rep to @pastel mirage @cold sorrel

[dusk bane]

I learnt a lot (:

[vestal hull]

Wait

😂

9=sqrt((-9)(-9)) = 3i x 3i = 9i^2 = -9

[pastel mirage]

we already explained how that could not be

[dusk bane]

can't split negatives under square roots

[vestal hull]

Rightt