The set of real numbers is not closed under powers. That is to say, there are some equations of the form y = xa which do not have a solution within the set. Typical example: x is negative, a = 0.5
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No difference. The set of complex numbers includes the set of imaginary numbers.
Yes, imaginary numbers are a subset of complex numbers.
No, it is imaginary. Irrational numbers are a subset of real numbers Real numbers and imaginary numbers are sets without any overlap.
They aren't imaginary.
It helps to visualize the numbers on a plane. The complex numbers occupy the entire plane. The real numbers are all the numbers on the horizontal axis, the imaginary numbers are all the numbers on the vertical axis. A complex number thus has a real and an imaginary part, a + bi, where a and be are real numbers (for example, 3 - 2i).