1. One way is to show the relationship between different components such as a
resistor and a coil. That would be R+iXL. This shows that the coil impedence is
90 degrees out of phase with R resistance.
2. Another way we can use complex numbers is as an aid to visualize the complex
fields around two conductors carrying current.
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Various engineering fields will use them. Electricity and electronics.
A complex number is any number that can be represented in the form of a+bi, the real numbers are a and b, the imaginary number is i. Complex numbers are used in scientific and engineering fields.
Real and Complex. Real numbers are your everyday numbers that most people are familiar with and Complex numbers are Real numbers mixed with imaginary numbers. Of course this is a VERY BROAD oversimplification, and the question is somewhat vague in that there are other "types" of numbers that are used, but I think this is the answer you are looking for.
Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.
No. Complex numbers is the highest set of numbers you can go, and there are no sets outside of complex numbers.