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Argument value in complex numbers in polar form.

  1. Sep 10, 2009 #1
    -1-(under root)3 i
    here we find that
    r=2(hypotenuse)
    a=-1(base)
    b=-(under root)3

    when i take sin theat= p/h=-(under root)3 / 2
    theat from sin is -60

    when i take cos theta = b/h =-1 / 2
    which gives 120

    now one is -60 and other is 120, which is the angel , i have to follow and what do i add it to?
     

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    Last edited: Sep 10, 2009
  2. jcsd
  3. Sep 10, 2009 #2

    HallsofIvy

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    Think about where [itex]-1- \sqrt{3}i[/itex] is on the complex plane. It has negative real part and negative imaginary part so it is in the third quadrant. Neither -60 or 120 degrees is in the third quadrant- they are both wrong.

    tan(theta)= -sqrt{3}/-1= sqrt(3) gives theta= 60 degrees but since this number is in the third quadrant, theta= 180+ 60= 240 degrees.

    cos(240)= -1/2 and sin(210)= -sqrt(3)/2.
     
  4. Sep 10, 2009 #3
    So the answer is :

    2{cos 120+ i sin 120)
    = 2 cis 120
    ??

    but my solution manual gave me this answer

    2 Cis 210
    which i myself think is wrong

    the table of cos and sin positive value is also used if i m right.and when cos and sin are yielding different results, we go to tangent.ok i get it now but i m lil confused because my solution manual gave wrong answer so please confirm.
     

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  5. Sep 10, 2009 #4
    2cis210 is incorrect. As HallsofIvy mentioned the correct argument is 240.

    --Elucidus
     
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