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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.
What else can I help you with?
Are there any other number systems?
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.
What are the applications of complex numbers?
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?
Why did humans create numbers?
Humans created numbers as a practical tool for counting, measuring, and recording quantities to facilitate trade, commerce, and resource management. The development of numbers allowed for more complex systems of communication, enabling societies to track time, manage agricultural cycles, and organize community activities. Over time, this numerical system evolved to include mathematical concepts that helped in problem-solving and scientific advancements, reflecting humanity's need for order and understanding in a complex world.
Are complex numbers the greatest number system?
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.
Why are imaginary numbers used in electronic systems control systems and physics?
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.
What is meant by demonstrating an understanding of the world as a set of related systems?
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
What number systems does 3.5 belong?
Rational numbers, real numbers, complex numbers and their supersets.
What number systems include the square root of 49?
Integers, rational numbers, real numbers, complex numbers, quaternions are some systems. Counting numbers is not a valid answer.
Are there any other number systems?
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.
Are all numbers complex?
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.
What is the significance of the Wolfram Equation in the field of mathematics and how does it contribute to our understanding of complex systems?
The Wolfram Equation is significant in mathematics because it helps us understand complex systems by providing a framework for studying patterns and behaviors in various systems. It contributes to our understanding by allowing us to analyze and predict the behavior of complex systems, such as weather patterns or biological processes, using mathematical principles.
What are the applications of complex numbers?
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?
What jobs involve complex numbers?
Mainly engineering, particularly control theory and other electronic systems; complex numbers are useful to represent oscillation frequency and phase information.
How do scientist increase their understanding of complex natural systems?
they use certain materials and instruments that may be hard to operate.
What are the strengths of systems theory?
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.
What is the term for understanding the whole of an organism by its parts?
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.
Why you study nonlinear systems when linear system is present?
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.
