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.

View More On Wikipedia.org
Recent contents Top users
  1. wolram

    Imaginary Engine: Dark Matter & Super Symmetry Needed

    My dream engine, needs a dark matter governor to prevent it exceeding its designed rpm limit, unfortunately no one makes them yet. It will produce dark energy as the motive power, but alas the formula for its production, or its existence is not known. It will, hypothetically, if it runs...
  2. N

    Mathematica Mathematica5.0 and I want to graph my equation that has imaginary part

    Hi can you help me guys? I use mathematica5.0 and I want to graph my equation that has imaginary part? Do you anyone plot equation that has imaginary part before? please help me:cry:
  3. J

    Solving for z with Complex Numbers

    All, I understand by rules of complex math, that raising a real number to the power of a complex number, you simply drop the imaginary part; it is not affected at all. But what happens when you raise a real number to the power of an imaginary. For instance... x = 2^3i - 2 Does x end...
  4. R

    Imaginary Normalisation Constant

    Homework Statement A one-dimensional system is in a state at time t=0 represented by: Q(x) = C { (1.6^0.5)Q1(x) - (2.4^0.5)Q2(x)} Where Qn(x) are normalised eergy eigenfunctions corresponding to different energy eigenvalues, En(n=1,2) Obtain the normalisation constant C The...
  5. O

    Stephen Hawking's Theory of Everything and Imaginary Time

    Hi, I am new here and have been lurking awhile. I have been reading Stephen Hawking Theory of Everything and it brought up imaginary time. ( I got this from the library and just saw online he did not endorse this book) It got me thinking. Time is based on Earth's observations to the solar...
  6. K

    Two things colliding at a imaginary moving surface

    Suppose you imagined a vertically aligned surface and with respect to this imagined (massless) surface were two objects shooting towards each other. Suppose these objects both had mass m, and each their kinetic energies (with respect to each other) would be .5mv^2. Suppose they are moving...
  7. T

    Wick rotation and imaginary number

    Can you use Wick rotation to turn any real variable to an imaginary one, not necessary time, such that your integration converges, and then, return back to the real? I'm not really sure how to use Wick rotation.
  8. P

    Solving Wave Equation / Imaginary Numbers

    Homework Statement Consider the simplified wave function: \psi (x,t) = Ae^{i(\omega t - kx)} Assume that \omega and \nu are complex quantities and that k is real: \omega = \alpha + i\beta \nu = u + i\omega Use the fact that k^2 = \frac{\omega^2}{\nu^2} to obtain expressions for \alpha and...
  9. B

    What is the absolute value of imaginary numbers, why not supernatural numbers?

    what is the absolute value of imaginary numbers, why not "queer" numbers? the square root of -1 is "i". the absolute value of an interger is itself, and of a negative number, it is a positive interger. |-5| = 5 |5| = 5 what is |5i| = ? |-5i| = ? why not invent a queer number...
  10. N

    Factoring Imaginary Numbers in a 2x1 Matrix: Solving the Physics Problem

    This is a physics problem but I am having trouble factoring this matrix. Basically, there shouldn't be anything left inside the matrix except 0's, 1's, or i's (any of which can be negative). This seems like such an easy problem but I cannot find something that works. Any ideas? \frac {1}...
  11. S

    Can All Functions Be Plotted on a Complex Plane?

    complex plane Hello, I was wondering if there are only specific types of forumlas that you can graph on a complex plane. I mean can you only plot recursive sequences such as the Mandelbrot Set or can you also plot x,y equations while just ignoring the real part of the y output. Thanks, -scott
  12. R

    Imaginary numbers entertwined with quadratics

    Hi, I'm not sure if this is calculas based or algebra based so here's the question. ( (A) 2i, -2i For this question i don't know what is being asked so i guess the pairs could be x... I know this: ax^2+bx+c, a(x-h)^2+k and a(x-s)(x-t) So the problem is how can i use the things that i...
  13. H

    Imaginary unit - electrical charge relationship

    In my Algebra 2 textbook it says that the imaginary unit finds practical application in electrical engineering. Is that because the imaginary unit is as elusive as electrical charge to rational perception?
  14. A

    State possible number of imaginary zeros help

    Ok, a multiple choice question wants me to: "State the possible number of imaginary zeros of g(x)=x^4+3x^3+7x^2-6x-13." (A) 3 or 1 (B) 2, 4, or 0 (C) Exactly 1 (D) Exactly 3 Using Descartes Rule of Sings I get: Exactly 1 positive zero, 3 or 1 negative zeros, and 0 or 2 Imaginary...
  15. S

    Imaginary multiplication with answer to be in polar (variables)

    I have to find (a+bi)(c+di) in polar form given that b,c,d>0 and a<0. So I convert each one to polar first. ( (a+b)cis(\arctan(-b/a) + \pi) ) ( (c+d)cis(\arctan(d/c)) ) That's as far as I got. Little help please?
  16. benorin

    Real & Imaginary parts of a finite product

    So I'm trying to work-out the real and imaginary parts of a finite product, put P_n = \prod_{k=1}^{n} \left( x_k + iy_k\right) where the x's and y's are real numbers like you would expect.
  17. S

    Derivative of an imaginary exponential

    Does anyone know how to take the derivative of e^((x^2)/i)? Thanks in advance!
  18. U

    Complex Function: Real & Imaginary Parts, Square, Reciprocal & Absolute Value

    I am to find the imaginary part, real part, square, reciprocal, and absolut value of the complex function: y(x,t)=ie^{i(kx-\omega t)} y(x,t)=i\left( cos(kx- \omega t)+ i sin(kx- \omega t) \right) y(x,t)=icos(kx- \omega t)-sin(kx- \omega t) the imaginary part is cos(kx- \omega t) the...
  19. D

    Why is Complex-Number Math Essential in Quantum Physics?

    Is "i" Really Imaginary? Complex-number math is very important in quantum physics. Is this because square roots of negative numbers are actual quantities being measured/calculated? Or is it that imaginary numbers aren't occurring for real, but complex math nevertheless represents very...
  20. U

    What is the imaginary part of each expression?

    I am supposed to identify the imaginary part (marked in bold) of each expression, just wanted to see if I got them correct: 1. (1+i)+(1-i) ......0 2. (5+i)+(1+5i) ......6 3. (5+i)-(1-5i) ......6 4. 1+2i+3+4i+5 ......6 5...
  21. G

    Imaginary Mass: Understanding Tachyons

    I'm having trouble with concept of imaginary mass, i just want to know why do we need the whole concept of tachyons
  22. D

    Does a wristwatch measure imaginary time?

    This is from "Exploring Black Holes" by Taylor and Wheeler. It's a very good book but I struggle not with the math, but the explanations (sometimes) On page B-13 is a frame called "Metric for the Rain Frame", which is a transformation of the Schwarzschild Metric from "bookkeeper coordinates"...
  23. K

    Real and Imaginary Parts of z+(1/z) - Have I Got This Right?

    Hi there have i got this right if someone could check please? z=x+\imath{}y Find the real and imaginary parts z+(1/z) sub x+\imath{}y + \frac{1}{x+\imath{}y} if we multiply by x+\imath{}y and i get as the real part as x^2-y^2+1. Have i got this right? Thanks in advance
  24. K

    Real & Imaginary Parts of z+(1/z) in x+\imathy

    z=x+\imathy Find the real and imaginary parts z+(1/z)
  25. E

    Imaginary Momentum: Physical Interpretation of Bound States

    Hi, When solving the delta potential Schrod. eq in momentum space, one finds that the poles of the wave function correspond to the bound states. This is the same result when solving the hydrogen atom in momentum space. However, the poles are when the momentum is pure imaginary. My...
  26. S

    Purely imaginary complex contour

    I've been working with Complex Analysis and have noticed an interesting result. Under what conditions will the following integral be purely imaginary: \int_{a-bi}^{a+bi} f(z)dz It seems to me some type of symmetry is required. Take for example: \int_{1-8i}^{1+8i} f(z)dz where...
  27. J

    Solving 2 inequalities with imaginary numbers?

    I have 2 equations, imaginary ones, and 2 unknowns...trying to solve for them..but the answer i got, works with one, but not the other: i*Z1 - i*Z2 = -2 - i Z1 + 3i*Z2 = 4 + 7i where i is the imaginary number, and Z1 and Z2 are the 2 unknowns the answer i got: Z1 : 1.33333 +...
  28. G01

    Whats wrong with this imaginary number problem?

    I saw this thing where someone proved that the imaginary number, i, the sqrt(-1) was equal to 1. here it is: i= sqrt(-1) i^2 = [sqrt(-1)]^2 i^2 = sqrt(-1) * sqrt(-1) i^2 = sqrt(-1*-1) i^2 = sqrt(1) i^2 = 1 so i = 1 I know there's something wrong here but i can't...
  29. Q

    Imaginary numbers past calculus level

    My teacher in the charter school I go to wanted to be a mathematition. He said calculus was no problem for him and he got past vector calculus, although he can't remember because it was so long ago. He said he got stuck on imaginary numbers past the caluclus level and this made him quit is...
  30. J

    Imaginary Number to Indicate Division by Zero?

    Forgive me if I'm being ignorant, but this recently occurred to me. We all know division by zero is undefinfed, but \sqrt {-1} used to be undefined too, until i was created. Has anyone ever proposed an imaginary number to indicate the result after division by zero?
  31. S

    Imaginary Vectors: Find Resultant & Solution Explained

    hi here's a questn: "2 vectors acting in same direction have resultant 20 whereas in perpendicular direction resultant is 10. find the vectors." pls. explain the imaginary solution.
  32. Mk

    Foster's Home for Imaginary Friends

    A while back, Huckleberry said he liked the show a lot, I watched it. Its great! Mac and Bloo! Yay! I try and catch it every chance I get, I recommend it. :approve: Thanks. :smile:
  33. cronxeh

    Auxiliary Equation with Imaginary Roots

    I was curious about what class would cover those types of Linear DE w Constant Coeff, particularly Hyperbolic Functions and exp z type of things. I remember my lecturer said back in Intro DE that we only covered first 2 types of Auxiliary Equations - real distinct roots and real repeated ones...
  34. motai

    Imaginary Girlfriends: Am I a Freak or Not?

    Alright.. I admit it. I have an imaginary girlfriend. :bugeye: Since I am obviously completely inept at this sort of stuff, I have resorted to my imagination to solve my emotional woes. Anyone else have imaginary girlfriends, or am I just a freak? :rolleyes:
  35. C

    What does imaginary time mean in spacetime separation?

    When I was reading the Landau's The Classical Theory of Fields, I found that when distance of four dimensional space is negative, the time's square should be a negative as well.Then time is an imaginary number. it's SPACELIKE. But what is imaginary time mean on earth? They say that in that...
  36. A

    Capacitor/Inductor Imaginary Numbers

    Dear All, Why do we introduce complex numbers when talking about the voltage behaviour through capacitors and inductors. Any help would be appreciated, Thanks
  37. D

    Imaginary Numbers: Solve i^(4/3) Equation

    Folks, I was just wondering why I can write: i^{4/3}=-\frac{1}{2}+i\frac{\sqrt{3}}{2} Regards
  38. S

    Frobenius method with imaginary powers

    I need to solve a linear, second order, homogeneous ODE, and I'm using the Frobenius method. This amounts to setting: y = \sum_{n=0}^{\infty} c_n x^{n+k} then getting y' and y'', plugging in, combining like terms, and setting the coefficient of each term to 0 to solve for the cn's. This...
  39. E

    Calculators Solving Imaginary Numbers with TI89 Calculator

    Well I know it can solve for real numbers of X^n+x^(n-1)+ etc etc = 0 But was wondering if it could also solve when there are imaginary numbers involved?... Thanks
  40. P

    What are Imaginary Numbers used for in mathematics?

    I have a very simple question. What are Imaginary Numbers (i.e. \sqrt[4]{-16}=2\mbox{i}) used for in mathematics besides negetive roots with an even index? Thank you in advance... ---- Life is a Problem... SOLVE IT!
  41. D

    Why were Imaginary numbers invented

    Why was i invented?
  42. Ivan Seeking

    Imaginary Playmates: A Look Into Childhood Mysteries

    http://seattlepi.nwsource.com/lifestyle/202632_imaginary07.html :rofl: :rofl: :rofl:
  43. S

    Help with imaginary and complex numbers

    If someone could give me some notes explaining about them that i could follow so i can do my homework and stuff it would be appreciated! I don't understand them at the moment b/c i don't understand the teacher, which is definately my problem. So it would be nice if i could get an explanation...
  44. E

    Epsilon Pi's ideas on imaginary numbers

    It is known that it was Descartes the one that gave the symbol i the connotation of imaginary; in electrical engineering there is the concept of apparent power(MVA) S = P + i Q where P(MW)=generation or consumed power and Q(MVAR) = reactive power and they both can be measured, so they...
  45. E

    Hermitian Operators and Imaginary Numbers

    So I understand what a hermitian operator is and how if A and B are hermitian operators, then the product of AB is not necessarily Hermitian since *Note here + is dagger (AB)+=B+A+=BA I also recognize that (AB-BA) is not Hermitian since (AB-BA)+=B+A+-A+B+ In addition, I know that...
  46. D

    Interpreting Imaginary Component Amplitudes in Fourier Series

    If you express a wave as a Fourier series like: z(x,t)= \sum _{n=1} ^{ inf.} A_n cos(nk_0 x - \omega (n) t ) Then what is the physical interpretation of a non-zero imaginary part of a component amplitude?
  47. N

    What is the purpose of imaginary numbers and how do they work?

    Sorry if this isn't the right forum, I didn't know so I just went to general. Could someone explain how this i (imaginary numbers) thing works? I know i is supposed to be a number which is the sqrt of a negative number, which isn't supposed to exist, but what's its use? And yeah...really any...
  48. I

    Real & Imaginary Parts of Complex Signals Explained

    Hey, I was wondering if anyone could explain to me the meaning of "real and imaginary parts of a complex signal"? Thanks Jay
  49. A

    Solving Imaginary Numbers: What is x^^2 = x^x = -4?

    I've been doing a lot of thinking about imaginary numbers lately. My first question was "What is sqr(i)?". I thought it was unsolvable until I punched it into my trusty (and often right) caclulator and found out it was (sqr(.5)i + sqr(.5))^2 So obvious now. Of course. Anyways, a...
  50. G

    UFO Sighting: Is It Real or Imaginary?

    I was outside just now, stargazing with my 10x40 binoculars, as it is an exceptionally clear and beautiful night here today. I was looking east, at Andromeda, when I spotted a moving object. It's apparent size and magnitude was about that of the stars behind. I follow it in my binoculars while...
Back
Top