- #1
Remixex
- 57
- 4
Homework Statement
First off i wasn't sure if i should put this in precalc or here so i just tossed a coin[/B]
I must find the roots of the expression z^4 +4=0 (which I've seen repeatedly on the internet)
Use it to factorize z^4 +4 into quadratic factors with real coefficients
The answer is (z^2 + 2z + 2)(z^2 - 2z + 2)
Homework Equations
Just the one given on the top
The Attempt at a Solution
Ok so, the question is quite basic as I've seen people pull it off in 10 mins, BUT after 3 semesters of dealing with only real numbers i forgot about complex ones, and now that i took complex analysis I'm in trouble D:
First off i had to search Euler's identity, that's how lost i was
I managed to establish that the magnitude of Z (r) is sqrt(2), i also got to the point where phi is -pi/4 +k*pi/2
so the 4 roots would be given by the sqrt(2) * e^i*phi given k takes the values within (0,1,2,3)
This is where i die i have no idea how to turn those into the final equation, i know the 4 solutions are
(+/-)1 (+/-)i, and from there is just polynomial algebra, but i don't know how to get there, Am i supposed to be able to deduct this as obvious from my last step?
Thanks in advance, i firmly believe there are no such thing as dumb questions, but given this is something I'm supposed to manage, it's quite the candidate :D