# How do you find all the real and complex roots of P(z)=z^4+1?

The roots of $P \left(z\right) = {z}^{4} + 1$ are
z^4+1=0=>z^4=-1=>z^4=e^(2pi*i+2kpi*i)=> z=e^(pi*i/4*(1+2k))
for $k = 0 , 1 , 2 , 3$
$z = \setminus \pm \setminus \frac{1 + i}{\setminus \sqrt{2}} , \setminus \setminus z = \setminus \pm \setminus \frac{1 - i}{\setminus \sqrt{2}}$