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 $a^{2}+b^{2}>c^{2}$.
Then, the correct statement is ().
(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
2. (B)

Statement (1) is correct. $a^{2}+b^{2}>c^{2}$ indicates that $a^{2}+b^{2}$ and $c^{2}$ are real numbers, therefore, according to the rule of transposition, we have $a^{2}+b^{2}-c^{2}>0$.

Statement (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 both real numbers, hence $a^{2}+b^{2}>c^{2}$ may not hold.
For example, take $a=2+i, b=i, c=\sqrt{2}+\sqrt{2}$, then we have
$$
a^{2}+b^{2}-c^{2}=(3+4 i)+(-1)-4 i=2>0,
$$

but it is not true that $a^{2}+b^{2}=2+4 i>4 i=c^{2}$.