Imaginary numbers are used in complex numbers that make some math simpler like electronics where there is a cycle frequency it makes the math much simpler to handle complex equations
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Mathematics is beautiful in itself. Back in the 1700s and later, mathematicians studied "imaginary" numbers (numbers that involve a factor of the square root of -1) knowing that they didn't describe anything "real", the way "real numbers" do. But when beauty can be melded to practicality, things get REALLY interesting. It turns out that you can use imaginary numbers and "complex numbers" (which have a "real" component and an "imaginary" component) to describe the way radiation and electromagnetic fields behave.
Yes, imaginary numbers are a subset of complex numbers.
No difference. The set of complex numbers includes the set of imaginary numbers.
That's difficult to say. Rafael Bombelli defined an imaginary number in 1572, but Rene Descartes actually gave the term imaginary. Nobody seemed to have much use for them until the work of Euler and Gauss in the 1700's and 1800's. This information I got from the Wikipedia article on Imaginary Numbers.
No, it is imaginary. Irrational numbers are a subset of real numbers Real numbers and imaginary numbers are sets without any overlap.