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Thread: complex numbers

  1. #1
    Feb 2009

    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

    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
    Nov 2008
    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 $\displaystyle 2\pi$ is significant. For example, if you had something like $\displaystyle 7\pi$, well that's just the same as $\displaystyle \pi$ because after you take out $\displaystyle 6\pi$ you have just 1 left.

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

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

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

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