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I suggest asking separate questions for complex numbers, and for matrices.
Complex numbers are used in a variety of fields, one of them is electrical engineering. As soon as AC circuits are analyzed, it turns out that complex numbers are the natural way to do this.
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What careers use complex numbers?
Engineering (especially electrical engineering), Math, Physics mainly.
Applications and use of complex numbers in engineering?
Any physical motion which is periodic, such as an oscillating beam, string, wire, pendulum, electronic signal, or electromagnetic wave can be represented by a complex number function. This can make calculations with the various components simpler than with real numbers and sines and cosines.
Jobs that require the use of imaginary numbers?
Physics (e.g., quantum mechanics, relativity, other subfields) makes use of imaginary numbers. "Complex analysis" (i.e., calculus that includes imaginary numbers) can also be used to evaluate difficult integrals and to perform other mathematical tricks. Engineering, especially Electrical Engineering makes use of complex and imaginary numbers to simplify analysis of some circuits and waveforms.
Why are imaginary numbers important?
They are used for working out equations where the numbers you are working with are not physically possible, but we just imagine they are, such as the square root of a negative number In engineering, especially Electrical Engineering, using complex numbers to represent signals (rather than sines and/or cosines) make comparing and working with signals easier.
What is complex math?
Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.
What is the physical significance of complex numbers?
They are frequently used in Engineering applications.
What jobs use complex numbers and how do they use them?
I suggest you read the Wikipedia article con complex numbers, specifically the section "Applications". One example is electrical engineering: in the case of AC, it helps to express all voltages, currents and impedances (equivalent of resistances) as complex numbers.
How will you use a complex number in your life?
As well as their use within mathematics, complex numbers have practical applications in many fields, including physics, chemistry, biology, economics, electrical engineering, and statistics.
Does the range of linear equations have all real numbers?
No. For example, linear algebra, for example, is about linear equations where the domain and range are matrices, not simple numbers. These matrices may themselves contain numbers that are real or complex so that not only is the range not the real numbers, but it is not based on real numbers either.
How are a numerator and denominator similar?
They are elements of of a set which may consist of integers, real or complex numbers, polynomial expressions, matrices.
What careers use complex numbers?
Engineering (especially electrical engineering), Math, Physics mainly.
What are considered complex numbers?
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.
Applications and use of complex numbers in engineering?
Any physical motion which is periodic, such as an oscillating beam, string, wire, pendulum, electronic signal, or electromagnetic wave can be represented by a complex number function. This can make calculations with the various components simpler than with real numbers and sines and cosines.
Why only square matrix have determinant?
The square matrix have determinant because they have equal numbers of rows and columns. <<>> Determinants are not defined for non-square matrices because there are no applications of non-square matrices that require determinants to be used.
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 use of imaginary axis in real life?
The imaginary axis is used in the definition of the complex numbers. Complex numbers are used in many fields in engineering, in particular - electric engineering, aerodynamics, acoustics etc.
Can The domain of all polynomials are all real numbers?
Yes, it cannot contain any imaginary numbers
