Why were imaginary numbers created?

Updated: 4/28/2022
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Originally, they were created so that every polynomial would have a solution. For example, the polynomial x² - 1 = 0 is a second order polynomial, so it should have 2 solutions. It does have 2 real solutions: 1 & -1. You can graph y = x² - 1 and see where the graph crosses the x-axis (these are the x coordinates that make y=0 and satisfy the equation). But what about x² + 1 = 0. If you graph y = x² + 1, it does not cross the x axis, but every polynomial is supposed to have a number solutions equal to the order {2nd order should have 2 solutions, 3rd order should have 3 solutions, etc.}

To handle polynomials like this, a number i was created such that i² = -1. Now this number i can be used to solve x² + 1 = 0. The solutions are x = i & -1. For many years, these numbers were considered just an imaginary concept, and for not much use until the work of Euler related them to sines and cosines. Now, imaginary and complex numbers are used to express the relationships between waves (in particular, electromagnetic waves and alternating current electricity).

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Q: Why were imaginary numbers created?
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Related questions

Are imaginary numbers irrational numbers?

No. Irrational numbers are real numbers, therefore it is not imaginary.

Which of these sets of numbers is not a subset of the real numbers irrational integer rational and imaginary?

Imaginary numbers are not a subset of the real numbers; imaginary means not real.

Can a complex number be imaginary?

Yes, imaginary numbers are a subset of complex numbers.

What is the difference between imaginary numbers and complex numbers?

No difference. The set of complex numbers includes the set of imaginary numbers.

Is the imaginary unit 8i irrational?

No, it is imaginary. Irrational numbers are a subset of real numbers Real numbers and imaginary numbers are sets without any overlap.

What are imagery numbers?

imaginary numbers are numbers that are a negative square root, which is not possoble therefor it is called and imaginary number. ex the square root of -24 is an imaginary number

Which number belongs to the set of imaginary numbers 2?

2 does belong to the set of imaginary numbers. Any real number is also imaginary. Imaginary numbers are the set of all numbers that can be expressed as a +b*i where "i" is the square root of negative one and "a" and "b" are both real numbers.

The symbol for imaginary numbers is?

An imaginary number is symbolized by the letter i

What type of problems have imaginary numbers?

Imaginary numbers are only ever used when you are using the square roots of negative numbers. The square root of -1 is i. You may find imaginary numbers when you are finding roots of equations.

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Imaginary Homelands was created in 1992.

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