Is there any example of a real world phenomenon modelled

Pamela Meyer

Pamela Meyer

Answered question

2022-01-18

Is there any example of a real world phenomenon modelled as x2+1=0, (or even a cubic equation) based on which Complex numbers were invented? What is the physical quantity which is square of itself and when added with 1 can become zero.

Answer & Explanation

Louis Page

Louis Page

Beginner2022-01-19Added 34 answers

A cuboid of volume 3 cubic metres has dimensions x metres by x2 metres by x+2 metres. What are the dimensions of the cuboid?
Cardano couldn’t solve a problem like this one. But the problem has a solution. It is approximately 2.303 metres by 0.303 metres by 4.303 metres.
Cardano’s method to find x was by evaluating the following expression:
32+131083+32131083.
The above number is, in fact, approximately 2.302776 ; yes, it is a real number, in spite of the 13108 written twice inside it. However, Cardano had no idea how to calculate 13108in order to solve the problem.
Hence, complex numbers were invented in order to solve this, and other similar problems.
Later on, of course, complex numbers ended up solving, or aiding in the solution or understanding of, a vast amount of other problems.

Thomas Nickerson

Thomas Nickerson

Beginner2022-01-20Added 32 answers

There are plenty of physical problems where the roots of x2+1=0 might come in handy to either construct a model of the real world, or to solve such a model. That’s where mathematics plays a role. And even in such a case the role of these roots is just a phase in the whole process; there are plenty of electrical engineers that use a spectrum and are quite capable of relating the spectrum to the original signal without the need to go through all the necessary calculations, which might involve computing a discrete Fourier transform (which does use the aforementioned roots).
Physics itself has some explaining to do as well. You probably know that the integral of v(t), the velocity, over an interval for time t is the displacement s(t). How about repeating this process and computing the integral of s(t) on the same interval?

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