Ok we have cosine of an angle corresponding to 1/2 and the sin corresponding to (sqrt3)/2 so the
θ in question should be ∏/3 (60 degrees).
The r = (1/2)^2 + (sqrt3/4)^2
r = 1/4 + 3/4
r = 1
No my book never mentioned anything about this, but it makes sense that we have a positive and a negative version of the root. That would give me four if I included the conjugates to the one I wrote, what would the 3rd set be??
Wicked alright let u = z^3
We have u^2 + u + 1 = 0
then u = -1/2 +- [(√3)/2]i
Now given that we took u = z^3, can I just cube the results to get the answers for z??
Homework Statement
Find all complex solutions of z^6 + z^3 + 1
(z^3 + 1)/(z^3 - 1) = i
Homework Equations
The Attempt at a Solution
I am going crazy with trial and error with these, there must be some systematic method or tricks that I am oblivious of. For the second question I...
It seems so, but the unit interval has cardinality c and at first glance it appeared to me that we were excluding a finite set from an infinite one, and if I am not mistaken with cardinal arithmetic, c would remain the cardinality. But it seems to be otherwise now.