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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.
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Where did complex and imaginary numbers come from?
The 16th century Italian mathematician, Gerolamo Cardano was the first to use imaginary and complex numbers in his work on cubic equations.
Why do you need imaginary numbers?
because somtimes there isn't an answer to every equation like what's the square root of -16.... there is no answer so we would just use an imaginary number which is i.It turns out that these are important in a practical sense. Imaginary numbers turn up all the time in quantum mechanics and certain types of electronic circuits as well.
Who are the mathematicians that discovered imaginary numbers?
The first person to write about them was Gerolamo Cardano in 1545, but he doesn't seem to have taken them seriously. See http://en.wikipedia.org/wiki/Gerolamo_Cardano . The first serious use of imaginary numbers (better, complex numbers) was by Rafael Bombelli, published in 1572. He used them as intermediate steps when solving cubic equations. See related link.
What are the real numbers that is not a whole number?
Real numbers are all numbers which do not contain "i", when "i" represents the square root of -1. All numbers which do contain "i" are "imaginary numbers" and are not real numbers. This means that all numbers you'd ordinarily use are real numbers - all the counting numbers (integers) and all decimals are real numbers. So in answer to your question, all the real numbers that are not whole numbers are all the decimal numbers - including irrational decimals such as pi.
What is the difference between infinitely many solutions and all real numbers?
Let me use an example. y^2 = -x (where y^2 means y squared) Then y = sq rt (-x). There is an infinite number of solutions, some of which are imaginary numbers and some are real. So when you say 'infinitely many solutions' this includes imaginary numbers. All real numbers is a subset of that.
What Jobs use complex conjugates?
Some of the jobs that use complex conjugates include quantum mechanics, electrical engineers and physicists. Complete understanding of generators and motors require the knowledge of imaginary numbers.
What jobs require you to use mathematics?
Any jobs that require a B.S.All jobs/careers involve the use of numbers.
Why do you use imaginary numbers?
grapes
What jobs use no numbers?
There are no jobs that don't use numbers?
What jobs use terminating decimals?
All jobs will use terminating decimals but most jobs will also require you to be able to work with recurring decimals and many will need decimal numbers which are neither terminating nor recurring.
Who was the first to use the symbol for imaginary numbers?
Isaac Newton
What types of jobs would require the use of a case skid loader?
There are a number of jobs that might require the use of a case skid loader. Many construction and building jobs would requite the use of a case skid loader or excavating jobs.
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.
What kind of jobs require a pneumatic torque wrench?
Jobs that require a pneumatic torque wrench include jobs that require mechanical work. This includes car mechanics, which use these wrenches to change lug nuts on a wheel.
What do imaginary numbers represent?
The real numbers together with the imaginary numbers form a sort of vector. What these complex numbers (complex means the combination of real and imaginary numbers) represent depends on the specific situation. Just as there are situations where it doesn't make sense to use negative numbers, or fractional numbers, in many common situations it doesn't make sense to use complex numbers. In an electrical circuit (specifically, AC), the real numbers might represent resistance, while the imaginary number represent reactance - and voltages and currents are also represented by complex numbers, with the angle of the complex number representing how much one quantity is ahead or behind another quantity (the "phase angle"). In quantum mechanics, the complex numbers might not represent anything (perhaps they don't, I am not sure...), but they are useful for calculations.
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.
Where did complex and imaginary numbers come from?
The 16th century Italian mathematician, Gerolamo Cardano was the first to use imaginary and complex numbers in his work on cubic equations.
