a) We are using the suggested notation.
Since we know that either or , and thus, in any case, implies
Since for all , we have
for all . Using chain rule, we get
Since
we conclude that
Therefore, satisfies Cauchy-Riemann.
b) The function has derivative
for all .
Since for all , the function is not injective, hence, not invertible either.
L. Assume that j : R-→ R-s C and satisfies what are known as the Cauchy-Riemann equations: (c) ...