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Homework Help: Complex number

  1. Aug 27, 2007 #1
    1. The problem statement, all variables and given/known data
    find the four fourth roots of -2[tex]\sqrt{3}[/tex]+i2

    i dont have any attempt for a solution because i dont know what to do..
    im really lost.. i regret sleeping in class
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Aug 27, 2007 #2


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    I imagine you were intended to use DeMoivres' theorem:
    If a complex number can be written in polar form [itex]z= r(cos(\theta)+ i sin(\theta))[/itex] then its nth power, zn, can be written [itex]z^n= r^n(cos(n\theta)+ i sin(n\theta)[/itex]
    In your case, n is the fraction 1/4. Convert [itex]-2\sqrt{3}+ 2i[/itex] to polar form (which happens to be pretty simple). Take the real fourth root of r. Remember that you can add any multiple of [itex]2\pi[/itex] to [itex]\theta[/itex]. Dividing by 1/4 will give you different results for different multiples of [itex]2\pi[/itex].
  4. Aug 27, 2007 #3
    im having some problem in the angle..
    what i dis is this

    z=r cis (theta)

    then, will i just substitute the numbers to the equation?
  5. Aug 28, 2007 #4


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    Yes, of course. r= 4 and theta= - 60 degrees (although I would prefer theta= -[itex]\pi/3[/itex]).
  6. Aug 28, 2007 #5
    i think the angle is is -30...


    tan (theta)= 2/[-2(sqrt3)]

    shouldn't I make the angle positive????

    if yes
    should i subtract 30 from 180
    or subtract 30 from 360?

    i'm totally clueless...
    desperately needing some help
  7. Aug 28, 2007 #6
    pls pls pls...help me with this one..can anyone give me a complete solution for this???thanks
  8. Aug 28, 2007 #7


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    Homework Helper

    It looks to me like your angle is more like 150 degrees. You are in the second quadrant. So yes, subtract it from 180.
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