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applicability: $\mathbb {R, C}$

Proposition: Complex Cauchy Sequences Vs. Real Cauchy Sequences

Let \((c_n)_{n\in\mathbb N}\) be a complex sequence \((c_n)_{n\in\mathbb N}\) is a complex Cauchy sequence, if and only if the real sequences of the real parts \((\Re(c_n))_{n\in\mathbb N}\) and imaginary parts \((\Im(c_n))_{n\in\mathbb N}\) are real Cauchy sequences.

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983