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Although most of us do not use imaginary numbers in our daily life, in engineering and physics they are in fact used to represent physical quantities, just as we would use a real number to represent something physical like the length of a stick or the distance from your house to your school.
In general, an imaginary number is used in combination with a real number to form something called a complex number, a+bi where a is the real part (real number), and bi is the imaginary part (real number times the imaginary unit i). This number is useful for representing two dimensional variables where both dimensions are physically significant. Think of it as the difference between a variable for the length of a stick (one dimension only), and a variable for the size of a photograph (2 dimensions, one for length, one for width). For the photograph, we could use a complex number to describe it where the real part would quantify one dimension, and the imaginary part would quantify the other.
In electrical engineering, for example, alternating current is often represented by a complex number. This current requires two dimensions to represent it because both the intensity and the timing of the current is important. If instead it were a DC current, where the current was totally constant with no timing component, only one dimension is required and we don't need a complex number so a real number is sufficient. The two key points to remember are that the imaginary part of the complex number represents something physical, unlike it's name implies, and that the imaginary number is used in complex numbers to represent a second dimension.
Remember, a purely imaginary voltage in an AC circuit will shock you as badly as a real voltage - that's proof enough of it's physical existence. I'll put a link in the link area to a great interactive site (it's actually my site but for it's educational purposes only) that explains the imaginary number utility more visually with animations.
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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.
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.
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.
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.
When do you use multiplication of negative numbers in real life?
It is possible to live a long and productive life without ever multiplying a negative number outside of a classroom.
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.
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 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.
How do you use complex and imaginary numbers in your daily life?
you would use complex and imaginary numbers in your daily life if you become a mathematician, electrical engineer, quantam mechanic, etc. otherwise, you would not use use them at all except in algebra 2, pre-calc, calculus....i hope that helped a little bit.
Why do you use imaginary numbers?
grapes
What can you formulate from the real numbers?
This question is kind of vague. Many of your everyday situations use the rational numbers (fractions and integers), which are a subset of real numbers. If you do anything with angles (like surveying, or navigation) then irrational (which are still real) come into play. There are situations when it's necessary to consider complex (a combination of real and imaginary) numbers. When dealing with waves or periodic motion, imaginary numbers become an important thing to consider.
How do you use odd numbers in real life?
well you use them for math
Is a million areal number?
There are two meanings for the phrase "real number". 1,000,000 is a real number no matter which of them you use. (Numbers that are not "real numbers" are "imaginary" or "complex" numbers if you're using the phrase in one sense, and "made-up" numbers like "a jillion" in the other sense.)
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.
Why is the square root of a negative number imaginary?
Any real number, when squared will give a positive real number. This is true weather you have a negative real number and square it, or positive. The concept of imaginary numbers was invented to handle equations which needed to use the square root of a negative number, in order to solve them.At first, they were not considered useful beyond this, so they were named imaginary numbers. Through the work of Euler and others, it became evident that imaginary and complex numbers could be useful, especially when analyzing waves, such as electrical waveforms.
How do you use real numbers in daily life?
For computations and Measurement ;))
What is the largest set of numbers that includes all the numbers ever used called?
set of real numbers? although people use imaginary numbers too, even though they're sort of the opposite of real numbers ... so maybe you're looking for the set of "all numbers"?
