A
At which points if any does the function
$f(z) = z\operatorname{Re}(z) + \bar{z}\operatorname{Im}(z)$ satisfy the Cauchy-Riemann equations?
B
At which points, if any is this function analytic. Justify your answer.
Answer
A. I applied the Cauchy Riemann equations and found that they are satisfied at x = 1, y = -1.
B. As they are not differentiable anywhere else in C, particularly in some neighbourhood of (1, -1), they function is analytic nowhere.
Are my answers for A and B correct?