$4 \cdot 2 a, b$ are real numbers, among the following five propositions, which one is correct?
(A) If $a>b$, then $a^{2}>b^{2}$.
(B) If $|a|>b$, then $a^{2}>b^{2}$.
(C) If $a>|b|$, then $a^{2}>b^{2}$.
(D) If $a^{2}>b^{2}$, then $a>b$.
(E) If $a \neq|b|$, then $a^{2} \neq b^{2}$.
(China Beijing Junior High School Mathematics Competition, 1983)
[Solution] Let $a=-2, b=-3$, then $-2>-3, |-2|>-3$, but $(-2)^{2}(-1)^{2}$, but $-2<-1$, so we know that $(D)$ is incorrect;

Let $a=-3, \quad b=3$, obviously $-3 \neq|3|$, but $(-3)^{2}=3^{2}$, hence $(E)$ is incorrect.
Therefore, the answer is ( $C$ ).