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

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Konstantinos Michailidis

Feb 27, 2016

The roots of #P(z)=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#

So finally the roots are

#z=\pm\frac{1+i}{\sqrt 2},\ \ z=\pm\frac{1-i}{\sqrt 2}#

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