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Solve certain bedeviling equations
- An imaginary number — basically, a number that, when squared, results in a negative number — was first established back in the 1400s and 1500s as a way to solve certain bedeviling equations.
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Imaginary numbers are not just a mathematical curiosity. They have real applications in physics, engineering and cryptography. Learn how they were invented, what they mean and how they work with BBC Science Focus Magazine.
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An imaginary number is the product of a real number and the imaginary unit i, [note 1] which is defined by its property i 2 = −1. [1] [2] The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. The number zero is considered to be both real and imaginary. [3]
Nov 21, 2023 · An imaginary number is a value that's the square root of a negative number. It can't exist on a one-dimensional number line. We'll explain.
- Imaginary numbers are numbers that, when squared, result in a negative number. The concept was first created in the 1400s and 1500s to solve comple...
- A complex number is a number that includes both a real part and an imaginary part. It's represented as a combination of a real number and an imagin...
- The complex plane is a two-dimensional plane where complex numbers are graphed. The horizontal axis represents the real part, and the vertical axis...
- The square roots of negative numbers involve the use of the imaginary unit 'i'. For example, the square root of -1 is i, and the square root of -9...
- Yes, imaginary numbers can be crucial in finding the roots of quadratic equations that have no real solutions.
- Imaginary and real numbers coexist within the broader concept of complex numbers. They can interact through operations like addition, subtraction,...
Jan 24, 2024 · Initially conceived to solve algebraic puzzles, imaginary numbers transcended their abstract origins to become indispensable in our understanding of the quantum world.
Aug 15, 2019 · “Imaginary” numbers are just another class of number, exactly like the two “new” classes of numbers we’ve seen so far. Let’s see why and how imaginary numbers came about.
Jul 1, 2022 · It was Gauss who made the distinction between imaginary numbers a*i and complex numbers a + b*i (a and b real). Up until his work, both complex and imaginary numbers had been termed imaginary.
Descartes coined the term imaginary: “For any equation one can imagine as many roots [as its degree would suggest], but in many cases no quantity exists which corresponds to what one imagines.” 9. John Wallis (1616-1703) notes in his Algebra that negative numbers, so long viewed with
