Olympiad Maths Prep

Track / Stage 4 / 102 of 340 #362 of 2000

Problem 362

AMC 12 late, AIME early
Algebra Difficulty 4.7 Find the answer

3. Let a,b,cCa, b, c \in \mathbf{C}, (1) If a2+b2>c2a^{2}+b^{2}>c^{2}, then a2+b2c2>0a^{2}+b^{2}-c^{2}>0 (2) If a2+b2c2>0a^{2}+b^{2}-c^{2}>0, then a2+a^{2}+ b2>c2b^{2}>c^{2}, which of the following is correct?
A. Both (1) and (2) are correct
B. (1) is correct, (2) is incorrect
C. (1) is incorrect, (2) is correct
D. Neither (1) nor (2) is correct

Official solution

3. B Imaginary numbers cannot be compared in terms of size

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.