Example 8 Given the following two propositions:
(1) Let $a, b, c$ all be complex numbers. If $a^{2}+b^{2}>$ $c^{2}$, then $a^{2}+b^{2}-c^{2}>0$;
(2) Let $a, b, c$ all be complex numbers. If $a^{3}+b^{2}-$ $c^{2}>0$, 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
(1994, National High School Mathematics Competition)
Analysis: From $a^{2}+b^{2}>c^{2}$, it is clear that $a^{2}+b^{2}$ and $c^{2}$ are real numbers, so $a^{2}+b^{2}-c^{2}>0$ is correct. Therefore, proposition (1) is correct.

From $a^{2}+b^{2}-c^{2}>0$, does it follow that $a^{2}+b^{2}>c^{2}$? Taking $a^{2}+b^{2}=5+3 \mathrm{i}, c^{2}=2+3 \mathrm{i}$, we see that proposition (2) does not hold. Hence, the correct choice is (B).