Explanation
In mathematics, the field of complex numbers C is an unordered field. This means that there is no natural definition of "greater than" (>) or "less than" (<) that is consistent with the ordering properties of real numbers.
The symbols > and < are only defined for real numbers.
Comparing two complex numbers like a+bi and c+di (where b,d=0) using inequality symbols is not defined in standard mathematics.
Analysis:
Statement I (1 + 4i > 3 + 2i): This inequality is invalid because complex numbers cannot be compared using inequality operators.
Statement II (2 + 3i < 3 + 4i): This inequality is also invalid for the same reason.
Statement III (4 + 3i > 3 + 4i): This inequality is also invalid.
Since none of these inequalities are mathematically valid, the number of valid inequalities is none.
Conclusion: The correct option is (a) None.
