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No, and integer is a whole number (ie has neither decimals nor fractions in it) an integer can, however be negative or even imaginary
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, but √-23 is. An imaginary number is the square root of a negative number.
A number with no decimals is called a whole number, or an integer.