- #1

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- 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