Complex mathematica tutorial?

  1. so i was kind of wondering if anyone knows of any mathematica tuorials for how to operate with complex numbers (i know how to do it by hand but solving a set of 5 equations all complex just seems suicidal :D )

    so any help d be appreciated
  2. jcsd
  3. CompuChip

    CompuChip 4,297
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    What about

    a^2 + b^2 == -2,
    b - 3 c == \[ImaginaryI],
    2 c - 3 a == 1 + \[ImaginaryI],
    d + 4 == Sqrt[e],
    e + a == -3},
    {a, b, c, d, e}

    just as you would solve a normal set of equations?
  4. chroot

    chroot 10,426
    Staff Emeritus
    Science Advisor
    Gold Member

    There's really nothing special at all about using complex numbers in Mathematica.

    - Warren
  5. CompuChip

    CompuChip 4,297
    Science Advisor
    Homework Helper

    By the way, if the equations are linear, there is nothing suicidal about it. Just write them in matrix form and row-reduce :smile: (the joy of every student)

    Oh, and before I forget, you make the imaginary i in Mathematica by typing I (capital i) or [Escape]ii[Escape]
    Last edited: Dec 10, 2007
  6. hmm yeah i wish they were linear

    well only problem i really got is that i dont know how to conjugate Exp[ i x] or to make shown as Cosx + i Sinx

    P.S equations were:
    a1 - a2 + b1 - b2

    -(20/197) Sqrt[2555] (a2 - b2) Sqrt[-1 + x] +
    20/197 Sqrt[2555] (a1 - b1) Sqrt[x]

    -a3 exp[20/197 \[ImaginaryI] Sqrt[2555] Sqrt[-2 + x]] +
    b2 exp[-(20/197) \[ImaginaryI] Sqrt[2555] Sqrt[-1 + x]] +
    a2 exp[20/197 \[ImaginaryI] Sqrt[2555] Sqrt[-1 + x]]

    -(20/197) Sqrt[2555] a3 Sqrt[-2 + x]
    exp[20/197 \[ImaginaryI] Sqrt[2555] Sqrt[-2 + x]] +
    20/197 Sqrt[2555]
    Sqrt[-1 +
    x] (a2 exp[20/197 \[ImaginaryI] Sqrt[2555] Sqrt[-1 + x]] -
    b2 exp[20/197 \[ImaginaryI] Sqrt[2555] Sqrt[-1 + x]])

    (dunno latex so sry for the uglyness)
    Last edited: Dec 10, 2007
  7. you can use ExpToTrig[...] to convert the exponentials to trigonometric functions.

    I think there is a conjugation function somewhere...
  8. CompuChip

    CompuChip 4,297
    Science Advisor
    Homework Helper

    You'd never guess it... it's called Conjugate[...]
    i.e. Conjugate[4 + 3I] gives 4 - 3I
  9. The mathematica help is pretty good, just do a search in the mathematica help browser for whatever you're trying to do, there is probably a function already designed for it.
  10. i think i actually managed it :D did the trig thingy and then used Conjugate (that one was silly obvious /blush)
    and i got a result

    thank you :)
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