Subject: Mathematical PhysicsTopic: Functions of A Complex Variable-Analytic FunctionAnswer the following functions and determine whether the following functions are Analytic. Please answer neatly and with details. 1 to 21. Use the Cauchy-Riemann conditions to find out whether the functions in Problems1.1 to 1.21 are analytic. Similarly, find out whether the following functions are analytic.23.x - iyx² + y²

Cauchy Riemann : According to the Cauchy Riemann ,the function is analytic if it follows the…

Answered: to 21. Use the Cauchy-Riemann…

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to 21. Use the Cauchy-Riemann conditions to find out whether the functions in Problems .1 to 1.21 are analytic. Similarly, find out whether the following functions are analytic. 23. x - iy x² + y²