Cauchy-Riemann Eqs: Show that f(z)=z^3 is Analytic everywhere and hence obtain its derivative.

To Show that f(z)=z^3 is Analytic everywhere and hence obtain its derivative. The Cauchy-Riemann equations are a set of two partial differential equations in complex analysis that relate the real and imaginary parts of a complex-valued function. These equations are named after Augustin-Louis Cauchy and Bernhard Riemann, two influential mathematicians in the field of complex analysis. The Cauchy-Riemann equations play a fundamental role in understanding and analyzing complex functions.

[monosizroy]

cr condition is not enough to prove that the function is analytic everywhere

[patnamsettysanjeevini]

Hlo sir y z=x+iy...y not polar form sir??