2. Given the following two propositions: (1). Let $a, b, c$ be complex numbers. If $a^{2}+b^{2}>c^{2}$, then $a^{2}+b^{2}-c^{2}>0$. (2). Let $a, b, c$ be complex numbers. If $a^{2}+b^{2}-c^{2}>0$, then $a^{2}+b^{2}>c^{2}$. Which of the following statements is correct?
(A) Proposition (1) is correct, and proposition (2) is also correct
(B) Proposition (1) is correct, and proposition (2) is incorrect
(C) Proposition (1) is incorrect, and proposition (2) is also incorrect
(D) Proposition (1) is incorrect, and proposition (2) is correct
(B)
2.【Analysis and Solution】Proposition (1) is correct. $a^{2}+b^{2}>c^{2}$ indicates that $a^{2}+b^{2}$ and $c^{2}$ are real numbers, thus, according to the rule of transposition, we have $a^{2}+b^{2}-c^{2}>0$.

Proposition (2) is incorrect. $a^{2}+b^{2}-c^{2}>0$ only indicates that $a^{2}+b^{2}-c^{2}$ is a real number, but it does not guarantee that $a^{2}+b^{2}$ and $c^{2}$ are real numbers, and it cannot ensure that $a^{2}+b^{2}$ and $c^{2}$ are both real numbers, hence $a^{2}+b^{2}>c^{2}$ does not necessarily hold.
For example, take $a=2+i, b=i, c=2 \sqrt{i}$, then we have
$a^{2}+b^{2}-c^{2}=(3+4 i)+(-1)-4 i=2>0$, but it does not follow that $a^{2}+b^{2}=2+4 i>4 i=c^{2}$.