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Math Help - complex numbers

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    7

    complex numbers

    agrument of z is the angle theta such that cos theta= x/z modulus and sin theta = y / z modulus. and it is only defined up to the addition of muliples of 2 pie.

    can u exaplin this statement
    "it is only defined up to the addition of muliples of 2 pie."

    One last question.
    express the following complex number in polar form

    i
    now r =1
    cos inverse= 0/2=90 * pie/180= pie /2
    sin inverse = 1/2= 30 *pie/180 =pie/6

    now answer is e ^ (ipie / 2)

    Question is why do we take theta value of pie/2 and not pie/6. i have done other questions as well. some time we take theta value which we get thrrough sin and some times the one we get through coz.WHY IS THAT ...PLZ HELP
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  2. #2
    Junior Member
    Joined
    Nov 2008
    Posts
    61
    For your first question, the wording is a little strange and confusing but what I think they're talking about is that only the part that's left over after a multiple of 2\pi is significant. For example, if you had something like 7\pi, well that's just the same as \pi because after you take out 6\pi you have just 1 left.

    For the second part, I'm confused as to how you got sin\theta =1/2. It should be sin\theta = 1 because

    i=(0)+(1)i=cos\theta + isin\theta

    so, cos\theta = 0 and sin\theta =1

    You take the value of theta that works for BOTH equations, in this case \theta =\pi /2
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