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Two Statements

Source: 1994 National High School Mathematics League, Exam One, Problem 2

February 28, 2020
complex numbers

Problem Statement

Give two statements: (1) a,b,ca,b,c are complex numbers, if a2+b2>c2a^2+b^2>c^2, then a2+b2−c2>0a^2+b^2-c^2>0. (2) a,b,ca,b,c are complex numbers, if a2+b2−c2>0a^2+b^2-c^2>0, then a2+b2>c2a^2+b^2>c^2. Then, which is true? (A)\text{(A)} (1) is correct, (2) is correct as well (B)\text{(B)} (1) is correct, (2) is incorrect (C)\text{(C)} (1) is incorrect, (2) is incorrect as well (D)\text{(D)} (1) is incorrect, (2) is correct
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