Problem

In Problem, answer true or false. If the statement is false, justify your answer by either...

In Problem, answer true or false. If the statement is false, justify your answer by either explaining why it is false or giving a counterexample; if the statement is true, justify your answer by either proving the statement or citing an appropriate result.

Consider a set of S of complex numbers. If the set A of all real parts of the numbers in S is bounded and the set B of all imaginary parts of the numbers in S is bounded, then necessarily the set S is bounded.

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