Final answer:
The set of complex numbers is closed under subtraction. Option 1: True is correct option.
Step-by-step explanation:
True. The set of complex numbers is closed under subtraction.
To show this, let's consider two complex numbers, A = a + bi and B = c + di.
The difference between A and B is given by (a + bi) - (c + di). Using the distributive property, we can expand this to a - c + (b - d)i.
Since the real and imaginary parts of A and B are both real numbers, the difference a - c and b - d are also real numbers. Therefore, the difference between two complex numbers is still a complex number, proving that the set of complex numbers is closed under subtraction.