1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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)
    x=-2(sqrt3)
    y=2
    r=4
    so
    theta=-60

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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...

    soln:

    x=-2(sqrt3)
    y=2
    r=4
    tan (theta)= 2/[-2(sqrt3)]
    =-1/sqrt3=-30degrees=-pi/6

    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

    Dick

    User Avatar
    Science Advisor
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Complex number
  1. Complex numbers (Replies: 36)

Loading...