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What are some imaginary numbers?
i is the Imaginary Unit, equal to sqrt(-1). So i and any real number multiplied by i will all be imaginary numbers. Here are some: i, -i, 5i, -3i, i*pi, etc.
Can a number be imaginary but not pure imaginary?
Yes. The number 1 + i is imaginary but not pure imaginary, while 5i is pure imaginary.
When were imaginary numbers invented?
Rafael Bombelli defined imaginary numbers in 1572, and Descartes named them 'imaginary' in 1637. It wasn't until the work of Euler in the 1700's that a usefulness for imaginary numbers was found, though. See the Wikipedia articles I linked for some good information on imaginary and complex numbers. I also linked an explanatory video that is pretty good as well.
What is the difference between imaginary numbers and complex numbers?
No difference. The set of complex numbers includes the set of imaginary numbers.
Is the difference of a complex number and its conjugate a real imaginary or pure imaginary number?
It is a pure imaginary number.Since (a+bi)-(a-bi) = 2bi, it is a pure imaginary number (it has no real component).
