# What is Imaginary: Definition and 362 Discussions

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, and its square is −25. By definition, zero is considered to be both real and imaginary.Originally coined in the 17th century by René Descartes as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Leonhard Euler (in the 18th century) and Augustin-Louis Cauchy and Carl Friedrich Gauss (in the early 19th century).
An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers a and b are called, respectively, the real part and the imaginary part of the complex number.

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1. ### B Is imaginary time a fourth dimension?

In a conversation Dr. Stephen Hawking said that he used Imaginary time as a 4th dimension to show that there was nothing before the big bang. How is it possible for Imaginary Time to act as a fourth dimension when it is still part of the ordinary time dimension?
2. ### I Proof of i-th Root of i: Analytic Connection?

I saw a proof in which they came up with the ith root of i through the typical algebra. $$i^{1/i} = i^{-i} = e^{i\frac{\pi}{2} \cdot -i} = e^{\frac{\pi}{2}} ~.$$ But it seems the proof is entirely algebraic, so we have no grounds for thinking it works anywhere. The only exception might be an...
3. ### I Does topology distinguish between real and imaginary dimensions?

Let's say we have four 3D spaces: (x, y, z) , (x, y, iz) , (x, iy, iz) and (ix, iy, iz), with i being the imaginary unit. Now, let's say we have a donut in each of these spaces. Geometrically, the donuts are different objects, have different equations and different properties (I think) but would...
4. ### B The Greatest Imaginary Mathematician of the 20th Century

https://scroll.in/article/946194/nicolas-bourbaki-one-of-the-greatest-mathematicians-of-20th-century-never-really-existed
5. ### B Tachyons and imaginary numbers?

https://www.scientificamerican.com/article/what-is-known-about-tachy/ How do tachyons have mass of a square root of a negative number? I thought this was not mathematically possible?
6. ### A Bessel functions of imaginary order

In Wikipedia article on Bessel functions there is an integral definition of “non-integer order” a (“alpha”). For imaginary order ia I get that Jia* = J-ia, where * is complex conjugate and ia and -ia are subscripts. Then in same article there is a definition of Neumann function, again for...
7. ### I Exploring Newton's Third Law in an Imaginary Magnetic Field

Hi, here's a theoretical problem that I am trying to find a satisfactory answer for. Imagine a coil that is temporarily switched on an off and generates a magnetic field that permeates through space. Now imagine a charged particle passing through this field, at time that the coil is already...

50. ### B Is infinity an imaginary number?

Is infinity a imaginary number?