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Table 1 Exact roots of functions \(f_{1}(x)\), \(f_{2}(x)\), and \(f_{3}(x)\)

From: On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

Exact-roots \(f_{1}(x)=x^{4}-ix^{2}+1\) \(f_{2}(x)=(1+2i)x^{5}+1-2i\) \(f_{3}(x)=x^{6}-ix^{3}+1\)
1 −8.9945 − 8.9945i −9.0353 + 4.2852i −1.0167 + 0.5870i
2 −8.9945 + 8.9945i −6.8676 − 7.2689i 0 − 1.1740i
3 −5.5589 + 5.5589i 1.2835 + 9.9173i 1.0167 + 0.5870i
4 5.5589 − 5589i 4.7909 − 8.7776i −0.7377 − 0.4259i
5 9.8285 + 1.844i 0 + 0.8518i
6 0.7377 − 0.4259i