Can. . . can someone please explain this to me?

Discussion in 'Random Topic Center' started by Professor_Chris, Nov 30, 2007.

8 league13 468 60
  1. Professor_Chris

    Professor_Chris Active Member

    This boggles my mind. There are so many things seemingly wrong with it, including raising a positive number to a power to arrive at a negative number. @_@;

    This is what I get for skimming through xkcd's archive. =(
     
  2. ShadowTogetic

    ShadowTogetic New Member

  3. Professor_Chris

    Professor_Chris Active Member

    I found this: Euler's Formula: e^ix = cos(x) + i * sin(x)

    Which means that e^2πi = 1. Crazy.
     
  4. ShadowTogetic

    ShadowTogetic New Member

    Guess that's good to know when I take the course
     
  5. Professor_Chris

    Professor_Chris Active Member

    Just to show how absurd it seems, e^2π is 535.491656.
     
  6. PokePop

    PokePop Administrator

    Anyone raised on pie made with square roots is going to be a negative one!
     
  7. ShadowTogetic

    ShadowTogetic New Member

    well, 535.49165552476473650 to be closer
     
  8. Professor_Chris

    Professor_Chris Active Member

    I just used google's calculator.

    This also means 535.49165552476473650^i = 1 = 535.49165552476473650^0
    and sqrt(535.49165552476473650)^i = -1.

    Another fun thing (535.49165552476473650^i)^i = 1^i
    But, (535.49165552476473650^i)^i = 535.49165552476473650^(i*i) = 535.49165552476473650^(-1) = 1/535.49165552476473650 = 0.00186744273 and 1^i = 1

    So, e^(2π*i*i) != (e^(2π*i))^i

    =(
     
    Last edited: Nov 30, 2007
  9. ShadowTogetic

    ShadowTogetic New Member

    I just used Mathematica for my result
     
  10. Magic_Umbreon

    Magic_Umbreon Researching Tower Scientist, Retired

    I'm confused; if you raise a number by the square root of -1, how many times are you multiplying or dividing by itself?

    I know a^2 = a multiplied by a
    and a^n is a multiplied by a an n number of times.

    So if the number is not real, how does it work?
     
  11. Mew*

    Mew* Active Member

    Imaginary numbers. They have an "i" after them. Depending on the exponential value on that i is, i could be equal to 1, i, -1, or, -i. You divide the exponential number by four, and the remainder determines its value. Then you multiply the value of i by its coefficient to find the value of that monomial. I hope I didn't mess anything up in that explanation >_<.
     
  12. ShadowTogetic

    ShadowTogetic New Member

  13. ryanvergel

    ryanvergel New Member

    You guys haven't taken calculus yet?

    and lol@pop
     
  14. ShadowTogetic

    ShadowTogetic New Member

    of course I have. Otherwise I wouldn't be able to take ODE
     
  15. Professor_Chris

    Professor_Chris Active Member

    I have taken Calculus. Two semesters of it. All we really covered was limits, differentiation, integration, and applications of those. I'm nearly certain we never touched on complex numbers in my Calculus classes.
     
  16. ShadowTogetic

    ShadowTogetic New Member

    Not sure if it varies with schools, but in Hunter, Intro to Complex Variables and Theories of Functions of a Complex Variable are courses offered. Prereq for the Intro is Vector Analysis
     
  17. Mew*

    Mew* Active Member

    No. I'm a little 9th grader. I'm only in Honors Advanced Algebra II. I'll get to Calculus in a few years!
     
  18. NoPoke

    NoPoke New Member

    seemingly is the key.

    The complex numbers are an extension of the real numbers. An extension that doesn't break the real number calculations but adds a great deal. Now if it was just more complicated (complex) then why bother, but it turns out that complex numbers are really usefull and actually simplify many calculations. e^itheta rules!

    -------

    Lots of math gets extended from what is taught at school. Did you know that you can have factorials of non-integral numbers?
    http://www.monroeccc.edu/mnaber/tests/FactorialsandGamma.pdf

    Madness! ... Did you know that factorial(-1/2) = sqrt(pi) :eek:

    Yep a factorial of a negative number and to make it worse its not even an integer. Mathemtics is nuts.:lol:
     
  19. Magic_Umbreon

    Magic_Umbreon Researching Tower Scientist, Retired

    Oh. My. God.

    That makes NO sense (I'm sure it does of course really it's just quite overwhelming because well everything I thought a factorial WAS it isn't lol).

    EDIT: A simple google search makes all clear
     
    Last edited: Dec 2, 2007
  20. Jim Ferrell

    Jim Ferrell New Member

    This entire discussion reminds me again of why I cannot stand math! :tongue:

    ~Jim
     

Share This Page