masudr said:Well, ultimately everything boils down to measurements of position: whether it's where the pointer is pointing to, or which LEDs are lit etc. The Ancient Greeks discovered (much to their dismay) that irrational numbers are realized in nature (e.g. the right-angled triangle with the two smaller unit sides has a hypotenuse of irrational length).
And so it was known, that the set of real numbers were realized in nature. There is no displacement in our space that is modeled by a complex number: this is why they have a slightly different status.
Imaginary numbers are numbers that can be expressed as a multiple of the imaginary unit, denoted by the letter "i". The imaginary unit is defined as the square root of -1.
Imaginary numbers are considered unobservable because they do not have a physical representation in the real world. They are purely conceptual and cannot be measured or observed directly.
Imaginary numbers are commonly used in science and mathematics to solve problems that involve complex equations and have no real solutions. They are also used in fields such as engineering, physics, and economics.
Yes, imaginary numbers do have real-world applications. They are used in a variety of fields such as signal processing, quantum mechanics, and electrical engineering. They also have applications in finance and economics, for example in modeling stock market fluctuations.
Complex numbers are numbers that have both a real and imaginary component, while imaginary numbers are solely composed of the imaginary unit. Complex numbers have both a real and imaginary axis on a graph, while imaginary numbers only exist on the imaginary axis.