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Axiomatic foundations: definition of complex numbers, their equality, sum and product. The field \(\mathbb {C}\) of complex numbers. The imaginary unit. Geometric representation of complex numbers. Moduli and conjugates. Triangle inequality. Polar form of complex numbers: cis function or symbolic exponential, de Moivre’s formula. Roots of complex numbers. Regions in the complex plane. The extended complex plane. Point at infinity.

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Complex Numbers

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  • 发表日期：

    2026年

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  • Carlo Presilla

摘要

Axiomatic foundations: definition of complex numbers, their equality, sum and product. The field \(\mathbb {C}\) of complex numbers. The imaginary unit. Geometric representation of complex numbers. Moduli and conjugates. Triangle inequality. Polar form of complex numbers: cis function or symbolic exponential, de Moivre’s formula. Roots of complex numbers. Regions in the complex plane. The extended complex plane. Point at infinity.