Analyticity and Cauchy-Riemann Equations

S. Sivakumar

Theoretical Studies Section, Materials Physics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102 INDIA

Cauchy-Riemann equations relate the real and imaginary parts of a complex-analytic function. These equations originate from the requirement for the uniqueness of the derivative, independent of the line or direction along which the limit is taken. This note attempts to make a presentation of the derivation in which the "direction of approach" is made explicit. Some interesting implications of the notion of analyticity are given