Complex numbers are defined as pairs of real numbers, represented as (a, b), where addition and multiplication are performed using specific rules. The discussion clarifies that the imaginary unit i, often defined as the square root of -1, cannot be simply understood in the same way as real numbers due to the ambiguity of square roots in complex numbers. Unlike real numbers, complex numbers do not have a natural ordering, which complicates their interpretation. The proper definition allows for the representation of complex numbers in the form a + bi, where i is identified with the pair (0, 1). This framework resolves the paradoxes associated with the square root of negative numbers by establishing a consistent arithmetic for complex numbers.