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SHASHWAT PRATAP SING
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If Imaginary numbers do exist and have real applications, then why do we call imaginary numbers "imaginary numbers"? . They exist. They're used all the time. What makes them "imaginary"?
The name originally was due to skepticism and has stuck. There is, however, an important distinction between real and complex/imaginary numbers in physics. Complex numbers tend to be part of the mathematical machinery, but measurements are always real numbers. You can measure an angle ##\theta##, but you can't do a measurement and get an imaginary angle ##i\theta##.SHASHWAT PRATAP SING said:If Imaginary numbers do exist and have real applications, then why do we call imaginary numbers "imaginary numbers"? . They exist. They're used all the time. What makes them "imaginary"?
Not what, whom! It was René Descartes 1637. The reason was very likely, that the complex zeros of polynomials, for which the imaginary numbers were first needed, couldn't be seen in their graphs.SHASHWAT PRATAP SING said:If Imaginary numbers do exist and have real applications, then why do we call imaginary numbers "imaginary numbers"? . They exist. They're used all the time. What makes them "imaginary"?
You did not. The correct version is in my post #4. Descartes used it 1637 for the first time. Mathematicians at this point in time were still busy to solve polynomial equations. Imaginary numbers occurred in the formulas of Italian mathematicians like Cardano, Tartaglia or Ferrari a century ago. Descartes, however, coined the name imaginary. If you want to know his thoughts, you have to dig up the original article, likely a letter.SHASHWAT PRATAP SING said:Please tell me have I understood it correctly...
fresh_42 said:Descartes, however, coined the name imaginary.
please help me i am confused i want to know why were these numbers called imaginaryhutchphd said:I prefer a more teleological approach: is the concept useful? Of course then one needs to define "useful
Look up Helmuth Gericke: Geschichte des Zahlbegriffs. Bibliographisches Institut, Mannheim 1970, p. 66. and the references therein.SHASHWAT PRATAP SING said:My question is not how , its why did he coined the name Imaginary if these numbers really exists.Help me.
Imaginary numbers are called "imaginary" because they were initially thought to be fictitious or imaginary, as they cannot be represented on a traditional number line. They were first introduced by mathematician René Descartes in the 17th century, who referred to them as "imaginary" to differentiate them from real numbers.
Yes, imaginary numbers do exist in mathematics. They are a fundamental part of complex numbers, which are used to solve certain equations that cannot be solved with real numbers alone. Although they may not have a physical representation, they have important applications in fields such as engineering, physics, and computer science.
Imaginary numbers are different from real numbers in that they include the imaginary unit "i", which is equal to the square root of -1. Real numbers, on the other hand, include all rational and irrational numbers that can be represented on a number line. Imaginary numbers cannot be graphed on a traditional number line, but they can be represented on a complex plane.
Imaginary numbers are important because they allow us to solve equations that cannot be solved with real numbers alone. They have many practical applications, such as in electrical engineering, where they are used to model alternating currents and in quantum mechanics, where they are used to describe the behavior of subatomic particles.
Yes, imaginary numbers can be used in the real world, despite their name. As mentioned before, they have important applications in various fields, such as engineering and physics. They can also be used to simplify complex mathematical calculations and represent certain physical phenomena, making them a valuable tool in problem-solving and understanding the world around us.