Using DeMoivre’s Theorem Assignment | Assignment Help Services

If z3−1=0z3-1=0, then we are looking for the cubic roots of unity, i.e. the numbers such that z3=1z3=1. If you’re using complex numbers, then every polynomial equation of degree kk yields exactly kk solution. So, we’re expecting to find three cubic roots. De Moivre’s theorem uses the fact that we can write any complex number as ρeiθ=ρ(cos(θ)+isin(θ))ρeiθ=ρ(cos(θ)+isin(θ)), and it states that, if z=ρ(cos(θ)+isin(θ))z=ρ(cos(θ)+isin(θ)), then zn=ρn(cos(nθ)+isin(nθ))zn=ρn(cos(nθ)+isin(nθ)) If you look at 11 as a complex number, then …

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