last day (15 days later) » 

Calvin Khor
Calvin Khor
09:41
Hi, did you get it?
MadSpaceMemer
MadSpaceMemer
Hey, an you just write me the answer to copy? I don't have time to put much thought in it. would really appreciate it.
no lol
Calvin Khor
Calvin Khor
Sorry, I'll give you the answer but I won't type up the full method
MadSpaceMemer
MadSpaceMemer
Alright fair enough !
Calvin Khor
Calvin Khor
( a/(a^2 + b^2 ) , -b/(a^2+b^2) )
MadSpaceMemer
MadSpaceMemer
thank you. I will put more thought to it today at night. but for now. that's quite good!
Calvin Khor
Calvin Khor
09:44
you're welccome
you can maybe first check what (a,b) funny product with (a,-b) is
this has less symbols
might be easier
MadSpaceMemer
MadSpaceMemer
i gotta to catch the bus in 30 minute
and i have 3 more questions xDD
Calvin Khor
Calvin Khor
dang
good luck
MadSpaceMemer
MadSpaceMemer
Thanks.maybe you can provide some more insights since you know your stuff?
Calvin Khor
Calvin Khor
sure, but: my internet is unstable so i can't see pictures and hopefully my connection doesnt drop... :)
MadSpaceMemer
MadSpaceMemer
this question reads
What is L when K = R?
i am thinking R^2?
Calvin Khor
Calvin Khor
09:57
haha...L is nothing but the complex numbers my friend
this is the reason for my first hint
writing (a,b) is just another way of writing a+bi
MadSpaceMemer
MadSpaceMemer
I am second weak in university. I don't know much :(
week(
Calvin Khor
Calvin Khor
i was
almost everyone is like that
MadSpaceMemer
MadSpaceMemer
So it is the complex numbers you are right. should i also argument why it is C?
Calvin Khor
Calvin Khor
hmm, you could explain that the multiplication is exactly the same as the multiplication of complex numbers, where a+bi is represented by (a,b)
MadSpaceMemer
MadSpaceMemer
And for the last question
And the most difficult
What can you say about $L$ when $X^2= -1$ in $K$ solvable?
Calvin Khor
Calvin Khor
10:03
hm, i'll need to think
MadSpaceMemer
MadSpaceMemer
Np i am quite happy with the ones i answered i don't need to answet this one :D
Calvin Khor
Calvin Khor
For the previous question, it may not be C
there is a field between Q and C that has a solution of x^2 = -1...it goes by the name A, it is the "algebraic closure" of Q....
MadSpaceMemer
MadSpaceMemer
we did not do that......
So i am guessing my professor will not torture us with stuff we did not discuss
Calvin Khor
Calvin Khor
but if the original field K was the real numbers, then it is C
for the last question, my gut feeling is that L is isomorphic as a field to K
MadSpaceMemer
MadSpaceMemer
could L be like a vector room of K if K is C?
Calvin Khor
Calvin Khor
10:08
yes, but I think what you can check is that L is a vector space of dimension 1 over C
which would prove that it is "equal" to C
MadSpaceMemer
MadSpaceMemer
Well mate i gotta run and catch the bus so i can deliver in time my answers or i will be rekt. You were an angel <3 thanks <3
Calvin Khor
Calvin Khor
you're welcome, glad to help

last day (15 days later) »