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Complex Derivatives

  • Unique Paper ID: 169517
  • Volume: 11
  • Issue: 6
  • PageNo: 1960-1965
  • Abstract:
  • In this paper, we explore the concept of complex differentiation with a particular focus on taking the i-th derivative, where i denotes the imaginary unit. By extend- ing the traditional methods of differentiation to the complex plane, we introduce new perspectives on differentiability, analyticity, and higher-order derivatives. The process of taking an i-th derivative leads to fascinating results that bridge real and complex analysis, offering insight into functions that exhibit complex periodicity and unique oscillatory behavior. Applications of the i-th derivative extend to fields such as quantum mechanics, signal processing, and complex systems, providing powerful tools for analyzing phenomena that cannot be captured by standard derivatives. This paper lays the groundwork for further exploration into fractional and complex-order calculus, highlighting both the theoretical and practical implications of complex derivatives.
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  • ISSN: 2349-6002
  • Volume: 11
  • Issue: 6
  • PageNo: 1960-1965

Complex Derivatives

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