Problem: Consider the statements: (I) (II) (III) (IV) , where we allow and to be real or complex numbers. Those statements for which there exist solutions other than and , are:
Answer Choices:
A. (I), (II), (III), (IV)
B. (II), (III), (IV) only
C. (I), (III), (IV) only
D. (III), (IV) only
E. (I) only
Solution:
is satisfied when , is satisfied when , and and are both satisfied when and is chosen arbitrarily. Therefore, ( ) is the correct choice.