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2.29.1  Exact bounds for complex roots of a polynomial :
complexroot

complexroot takes 2 or 4 arguments : a polynomial and a real number є and optionnally two complex numbers α,β.
complexroot returns a list of vectors.

To find the roots of x3+1, input:

complexroot(x^3+1,0.1)

Output :

[[-1,1],[[(4-7*i)/8,(8-13*i)/16],1],[[(8+13*i)/16,(4+7*i)/8],1]]

Hence, for x3+1 :

To find the roots of x3+1 lying inside the rectangle of opposite vertices −1,1+2*i, input:

complexroot(x^3+1,0.1,-1,1+2*i)

Output :

[[-1,1],[[(8+13*i)/16,(4+7*i)/8],1]]

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