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Yes. The number 1 + i is imaginary but not pure imaginary, while 5i is pure imaginary.
It is a pure imaginary number.Since (a+bi)-(a-bi) = 2bi, it is a pure imaginary number (it has no real component).
no
A complex number can be a pure imaginary, or a pure real number, or a combination of the two. The form for a complex number is a + bi, where a & b can be any real numbers (so if a = 0, then the number is pure imaginary; and if b=0, then it is a real number).
Yes, imaginary numbers are a subset of complex numbers.