Example of a function that satisfies the Cauchy-Riemann equation - Lecture III

Example of a function that satisfies the Cauchy-Riemann equation.

In this lecture Dr. Kamran Khan takes his time to solve a problem that satisfies the Cauchy-Riemann equation. 

The question says, show that the function

$f(z)=\frac{x^3(1+i)-y^3(1-i)}{x^2+y^2}$ satisfies the Cauchy-Riemann equation at $z=0$ but $f'(0)$ does not exist.

Watch video below

Kamran Khan is an assistant professor at the department of mathematics, Aligarh Muslim University, Aligarh India.

You can subscribe to his channel on YouTube @ Dr. Kamran Khan