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Theory and Modern Applications

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