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z=x+iy, where x and y are real numbers. Complex numbers can produce interesting graphs. If you graphed the above, you would get vertical and horizontal lines. But what happens when you graph 1/z ? When you work it out, you get two equations which are at right angles to each other. You get u=x/(xx+yy) and v=-y/(xx+yy) which are families of concentric circles at right angles to each other.
3i. Combining the real number 3 with the imaginary number i creates a complex number.

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Q: What are examples of complex numbers?
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Solved examples of bi complex numbers?

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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 is the relation of complex numbers to real numbers?

Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.


Could anyone list numbers not in the set of complex numbers?

No. Complex numbers is the highest set of numbers you can go, and there are no sets outside of complex numbers.


Set of real numbers and set of complex numbers are equivalent?

Real numbers are a proper subset of Complex numbers.