| 单词 | imaginary number |
| 例句 | Then imaginary numbers are represented by a line going up and down the page, with i, 2i, etc. above the middle, and —i, —2i, etc. below. A Brief History of Time: And Other Essays 1988-01-01T00:00:00Z Descartes thought that these numbers were even worse than negative numbers; he came up with a scornful name for the square roots of negatives: imaginary numbers. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z That is to say, for the purposes of the calculation one must measure time using imaginary numbers, rather than real ones. A Brief History of Time: And Other Essays 1988-01-01T00:00:00Z Thus imaginary numbers are in a sense numbers at right angles to ordinary real numbers. A Brief History of Time: And Other Essays 1988-01-01T00:00:00Z “If you use imaginary numbers, you don’t need to know where ‘C’ is to find ‘T.’ The Smartest Kid in the Universe 2020-12-01T00:00:00Z “What do you know about imaginary numbers, plane geometry, and vector algebra, Jake?” The Smartest Kid in the Universe 2020-12-01T00:00:00Z Like imaginary numbers, we can’t see them or feel them or smell them, even though they are necessary for doing calculations. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z This is only true if you accept imaginary numbers as well as real numbers. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z In this composer’s rarefied world, impulse overrules inhibition; cause and effect are for naïfs; one plus two equals an imaginary number. Why a fashionable young audience flocked to hear an obscure Greek composer's soundscape 2017-04-25T04:00:00Z We never glimpse this band, but when Catherine grudgingly admires the group’s song about imaginary numbers, we long to hear it, too. Review | Seamless cast in a gripping ‘Proof’ at Olney 2017-05-22T04:00:00Z By way of projecting a federal budget deficit into both the near and distant future, the season’s presidential candidates float cloud-capped towers of imaginary numbers destined to leave not a rack behind. My book was a bad idea 2012-06-27T00:00:00Z "Can you think of examples from the world we live in now, inventions that exist because of imaginary numbers?" he pleaded. The Brown Years; Chris Moyles; In Our Time 2010-09-25T23:06:00Z Last week's programme, on imaginary numbers, made me gleeful. The Brown Years; Chris Moyles; In Our Time 2010-09-25T23:06:00Z That infinities, infinitesimals, imaginary numbers or other unusual number spaces can be difficult to describe may not seem too surprising. These Are the Most Bizarre Numbers in the Universe 2023-05-23T04:00:00Z Later, complex numbers, which are the sum of a real and an imaginary number, gained wide acceptance by mathematicians because of their usefulness for solving complicated mathematical problems. Quantum Physics Falls Apart without Imaginary Numbers 2023-04-24T04:00:00Z It's hard to wrap your head around imaginary numbers. The Best Habitats for Whales, Leopards and Office Workers 2023-03-14T04:00:00Z Wireless, cellular and radar technologies utilize imaginary numbers. College Algebra with Corequisite Support 2020-09-23T00:00:00Z We want our result to be in standard form with no imaginary numbers in the denominator. Intermediate Algebra 2020-05-06T00:00:00Z The imaginary number is defined as the square root of negative 1. Precalculus 2021-12-01T00:00:00Z Our finding means that imaginary numbers are an essential ingredient in the standard formulation of quantum theory: without them, the theory would lose predictive power. Quantum Physics Falls Apart without Imaginary Numbers 2023-04-24T04:00:00Z If the value in the radicand is negative, the root is said to be an imaginary number. Algebra and Trigonometry 2015-02-13T00:00:00Z Electrical engineers use imaginary numbers to measure the amplitude and phase of electrical oscillations. College Algebra with Corequisite Support 2020-09-23T00:00:00Z Now that we are familiar with the imaginary number i, we can expand the real numbers to include imaginary numbers. Intermediate Algebra 2020-05-06T00:00:00Z Imaginary numbers are distinguished from real numbers because a squared imaginary number produces a negative real number. Precalculus 2021-12-01T00:00:00Z Does this imply that imaginary numbers exist in some way? Quantum Physics Falls Apart without Imaginary Numbers 2023-04-24T04:00:00Z A complex number is the sum of a real number and an imaginary number. Algebra and Trigonometry 2015-02-13T00:00:00Z The Schrödinger equation, for example, employs so-called imaginary numbers, multiples of the square root of –1. I'm Agonizing over My Naive Realism 2021-03-19T04:00:00Z If b ≠ 0, then a + bi is an imaginary number. Intermediate Algebra 2020-05-06T00:00:00Z Complex numbers are a combination of real and imaginary numbers. Precalculus 2021-12-01T00:00:00Z Schrödinger insisted this version was the “true” theory and that imaginary numbers were merely for convenience. Quantum Physics Falls Apart without Imaginary Numbers 2023-04-24T04:00:00Z Imaginary numbers differ from real numbers in that a squared imaginary number produces a negative real number. Algebra and Trigonometry 2015-02-13T00:00:00Z My efforts to understand how imaginary numbers map onto the real world have led me, perversely, in the opposite direction. I'm Agonizing over My Naive Realism 2021-03-19T04:00:00Z If a = 0, then a + bi becomes 0 + bi = bi, and is called a pure imaginary number. Intermediate Algebra 2020-05-06T00:00:00Z Give an example to show the product of two imaginary numbers is not always imaginary. Precalculus 2021-12-01T00:00:00Z The dollar values of the contracts that will be announced next week are widely known to be the most imaginary numbers in all of free agency. In N.F.L. Free Agency, Your Team Either Goes Broke or Stinks 2021-03-10T05:00:00Z Complex numbers consist of real and imaginary numbers. Algebra and Trigonometry 2015-02-13T00:00:00Z Instead of imaginary numbers becoming more real, real numbers, which fall on a line extending from positive to negative infinity, are becoming less real. I'm Agonizing over My Naive Realism 2021-03-19T04:00:00Z It is made up of both the real numbers and the imaginary numbers. Intermediate Algebra 2020-05-06T00:00:00Z That’s an appropriate label, because an imaginary number consists of the square root of a negative number, which by definition does not exist. Is the Schrödinger Equation True? 2021-01-07T05:00:00Z Ordinarily, but quantum vectors are often expressed as complex numbers, which contain imaginary numbers, based on the square root of negative one. Quantum Escapism 2020-08-22T04:00:00Z Give an example to show that the product of two imaginary numbers is not always imaginary. Algebra and Trigonometry 2015-02-13T00:00:00Z After all, there are still plenty of careers that don’t require expertise in the meaning of imaginary numbers or the minutiae of quadratic equations. I only took three years of high school math, escaped with a 'D' and turned out OK 2020-02-13T05:00:00Z The complex number system includes the real numbers and the imaginary numbers. Intermediate Algebra 2020-05-06T00:00:00Z It was only later that people came up with the concepts of negative numbers, zero and even more esoteric concepts like imaginary numbers — the square roots of negative numbers. This professor’s ‘amazing’ trick makes quadratic equations easier 2020-02-10T05:00:00Z For example, the solutions to x5 = 1 are five points on a circle when plotted onto a graph comprised of real numbers along one axis and imaginary numbers on the other. ‘Grand unifying theory of maths’ nets Abel Prize 2018-03-19T04:00:00Z Unlike the solutions for ocean breakers or sound, wave functions always contain imaginary numbers. Nil Communication: How to Send a Message Without Sending Anything at All 2017-06-27T04:00:00Z Yet imaginary numbers proved a powerful invention, and modern physics and engineering could not function without them. The Singular Mind of Terry Tao 2015-07-24T04:00:00Z Thus counting backward led to zero and to the negative numbers; the inversion of involution to the imaginary numbers. International Congress of Arts and Science, Volume I Philosophy and Metaphysics 2011-12-12T03:00:31.160Z Functions of Complex Variables, wherein complex or imaginary numbers are involved. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 "Frost" to "Fyzabad" 2011-08-15T02:00:28.473Z "It's an imaginary number based on Social Security." What does 65 mean? 2011-07-11T16:50:04Z When the moderator asked Kroto whether it is possible to describe the power of imaginary numbers in words, his answer was simple and short. Lindau Nobel Meeting--Shakespeare and Beethoven and buckminsterfullerene for the uninitiated 2011-07-03T22:45:06.357Z Now from a quadric equation we derive, in like manner, the notion of a complex or imaginary number such as is spoken of above. Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 7 "Equation" to "Ethics" 2011-02-27T03:00:31.973Z He was subconsciously bending his fingers as if they were clasping the Nokia 3660, and he was tapping imaginary numbers into his palm. An Apostate: Nawin of Thais He explored imaginary numbers such as the square roots of negative numbers. Our Legal Heritage : 600-1776 King Aethelbert - King George III There were now negative numbers, irrational numbers, and imaginary numbers. Our Legal Heritage There were now negative numbers, irrational numbers such as square roots, and imaginary numbers such as square roots of negative numbers. Our Legal Heritage : 600-1776 King Aethelbert - King George III |
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