Pick the correct statement(s) from below. (A) If $f ( z )$ is a function defined on $\mathbb { C }$ that satisfies the Cauchy-Riemann equations at $z = 0$, then $f ( z )$ is complex-differentiable at $z = 0$. (B) The function $\frac { ( \sin z - z ) \bar { z } ^ { 3 } } { | z | ^ { 6 } }$ is holomorphic on $\{ z \in \mathbb{C} : 0 < | z | < 1 \}$ and has a removable singularity at $z = 0$. (C) There exists a holomorphic function on $\{ z \in \mathbb { C } : | z | > 3 \}$ whose derivative is $\frac { z } { ( z - 2 ) ^ { 2 } }$. (D) There exists a holomorphic function on the upper half plane $\{ z \in \mathbb { C } : \mathfrak { I } z > 0 \}$ whose derivative is $\frac { z } { ( z - 2 ) ^ { 2 } \left( z ^ { 2 } + 4 \right) }$.
Pick the correct statement(s) from below.\\
(A) If $f ( z )$ is a function defined on $\mathbb { C }$ that satisfies the Cauchy-Riemann equations at $z = 0$, then $f ( z )$ is complex-differentiable at $z = 0$.\\
(B) The function $\frac { ( \sin z - z ) \bar { z } ^ { 3 } } { | z | ^ { 6 } }$ is holomorphic on $\{ z \in \mathbb{C} : 0 < | z | < 1 \}$ and has a removable singularity at $z = 0$.\\
(C) There exists a holomorphic function on $\{ z \in \mathbb { C } : | z | > 3 \}$ whose derivative is $\frac { z } { ( z - 2 ) ^ { 2 } }$.\\
(D) There exists a holomorphic function on the upper half plane $\{ z \in \mathbb { C } : \mathfrak { I } z > 0 \}$ whose derivative is $\frac { z } { ( z - 2 ) ^ { 2 } \left( z ^ { 2 } + 4 \right) }$.