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How To Evaluate Complex Numbers

  1. Dec 2, 2009 #1
    Hi PFs



    i want to know how to evaluate the complex number, and what are the meaning of the evaluating a complex number



    Let Z be the complex number, Z = (3-4i)^5 what i have to do, just give me hint
     
  2. jcsd
  3. Dec 2, 2009 #2

    sylas

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    Put the complex number into its polar representation: r.e.
     
  4. Dec 2, 2009 #3
    its polar representation is Z = r[Cos(thita) + iSin(thita)]
    is it is Evaluation
    i want to know what actually i have to do in evaluation
    Thanks for your help :)
     
  5. Dec 2, 2009 #4

    sylas

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    You need to go in the reverse direction, using x and y as your variables, not r and θ. Can you complete the following with substitutions for r and θ in terms of x and y?

    [tex]r^{i\theta} = x + iy[/tex]​

    Alternatively, can you rewrite 3-4i into polar form, to, say, four decimal places?

    Cheers -- sylas
     
  6. Dec 2, 2009 #5
    i was thinking that evaluation is like polar form i don't know how to resolve this, i know nothing about
    [tex] r^{i\theta} = x + iy [/tex]
    please tell me what i have to do,
     
  7. Dec 2, 2009 #6

    HallsofIvy

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    To find powers you need "DeMoivre's formula":
    [tex](r[cos(\theta)+ i sin(\theta)])^n= r^n (cos(n\theta)+ i sin(n\theta))[/tex].

    If DeMoivre's formula is not in your text, did you consider just sitting down and multiplying 3- 4i by itself 5 times? That would probably have been faster.
     
  8. Dec 2, 2009 #7
    oOps this is like that yes Demorvies theorem is in mine book, i have to apply this, and is n will the power like 0,1,2....n
     
  9. Dec 2, 2009 #8

    sylas

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    I fool so feelish....

    HallsofIvy is quite right; simply multiplying it is probably the easiest thing to do when you have an integer exponent.

    For example:
    [tex](3-4i)(3-4i) = 9 - 24i + 16i^2 = 9 - 16 - 24i = -7 -24i[/tex]​
    Keep going from there. Multiply by (3-4i), and again, and once more. You don't need the polar form.

    However, since I mentioned it, I'd better go ahead with the answer:
    [tex]\sqrt{x^2+y^2} \times e^{\text{atan2}(y, x) i} = x + iy[/tex]​
    You don't need to worry about this if you take HallsofIvy's hint about repeated multiplications.

    Cheers -- sylas
     
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