The set $A = \left\{ ( z , w ) \in \mathbb { C } ^ { 2 } \mid z ^ { 2 } + w ^ { 2 } = 1 \right\}$ is bounded in $\mathbb { C } ^ { 2 }$.
The set $A = \left\{ ( z , w ) \in \mathbb { C } ^ { 2 } \mid z ^ { 2 } + w ^ { 2 } = 1 \right\}$ is bounded in $\mathbb { C } ^ { 2 }$.