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I would say that you would need to demonstrate that you understand that i is a number which when squared equals -1. Also demonstrate how complex numbers can be represented graphically, both as rectangular coordinates an polar coordinates. Another thing would be an understanding of Euler's relationship: e^(i*Θ) = cos(Θ) + i*sin(Θ). Note that Θ must be in radians for this to work.

Q: How can one demonstrate the understanding of real and complex numbers systems?

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There are many number systems. The real numbers, the rational numbers, the complex numbers and some more esoteric ones such as p-adic numbers are all number systems.

There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?

The set of complex numbers encompasses real, imaginary, and combinations of the two, so it is the largest set that you are likely to encounter. There are other number systems, such as quaternion imaginaries, which you may never encounter, so I only mention it here and you can look it up for more info if you're interested.

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.

Numbers that can be positive or negative include the integers, the rational numbers, the real numbers, and the complex numbers. All integers are rational numbers (numbers that can be written as a fraction, like 2/1), but most rational numbers are not integers -- like -1/2. (2/1, a rational, can be written as 2, an integer). The real numbers include all the rationals, plus many, many more numbers that can't be written as ratios or fractions, such as the square root of 2, pi, and the euler constant, e. As with the rational numbers and integers, there are as many negative real numbers as there are positive ones. Finally, we have the complex numbers. These include all of the real numbers, plus the roots of negative real numbers. Complex numbers are written in two parts -- a real part, plus an "imaginary" part (which is just as "real" as the real part, but is called "imaginary" for historical reasons). For example, 1 + i is a complex number with positive real and imaginary parts, while -1 - i is a complex number with negative real and imaginary parts. Positive and negative number systems are clearly very important in mathematics and in everyday life. They are all distinguished by the fact that they include magnitudes less than zero, as well as greater than zero (magnitudes of complex numbers are more complicated because complex numbers can have both positive and negative parts in one complex number!) There is also the term "non-zero" which refers to values that are positive or negative but not a value that is neither. It is a very important mathematical term since many functions (reciprocals, for example) can only have non-zero domains.

Related questions

Demonstrate an understanding of the world as a set of related systems by recognising that the business organisation is one of the systems in this network of systems and that problemsolving-contexts in an organisation do not exist in isolation

Rational numbers, real numbers, complex numbers and their supersets.

Integers, rational numbers, real numbers, complex numbers, quaternions are some systems. Counting numbers is not a valid answer.

There are many number systems. The real numbers, the rational numbers, the complex numbers and some more esoteric ones such as p-adic numbers are all number systems.

There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?

The answer is Yes, for the purposes of most Math students. There are, number systems that have been devised which are outside the set of Complex Numbers, though.

Mainly engineering, particularly control theory and other electronic systems; complex numbers are useful to represent oscillation frequency and phase information.

they use certain materials and instruments that may be hard to operate.

Systems theory provides a holistic perspective by focusing on relationships and interactions among components. It emphasizes understanding complex systems as a whole, rather than just the individual parts. Systems theory is also flexible and can be applied across various disciplines to analyze and solve complex problems.

Reductionism is the term for understanding the whole of an organism by its parts. It involves breaking down complex systems into simpler components to better understand how they function.

Linear systems are easier to understand and help you build an understanding of the workings of a system. Once you have a firm understanding of linear systems and the mathematics are understood you will be in a better position to understand more complex non-linear systems.

Advances in Complex Systems was created in 1998.