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Cancelling confusion

  1. Jul 3, 2007 #1
    hi

    i'm confused at to how my textbook has done the following cancelling :S. hope you can clear things up for me :D

    thnx

    context: im looking at complex numbers and De Moivre's Theorem and its consequences Ill use \oslash as the "arguement".

    1. [tex]z_{1}z_{2} = r_{1}r_{2}(cos\oslash_{1}cos\oslash_{2} - sin\oslash_{1}sin\oslash_{2} + i(cos\oslash_{1}sin\oslash_{2} + sin\oslash_{1}cos\oslash_{2}))[/tex]

    which then cancels to

    [tex]z_{1}z_{2} = r_{1}r_{2}(cos(\oslash_{1} + \oslash_{2}) + isin(\oslash_{1} + \oslash_{2}))[/tex]

    I see how the [tex]cos(\oslash_{1} + \oslash_{2})[/tex] gets there, but not sure whats going on with the rest :S.

    2. [tex]\frac{1}{z} = \frac{1}{r}*\frac{cos\oslash-isin\oslash}{(cos\oslash+isin\oslash)(cos\oslash-isin\oslash)}[/tex]

    cancels to

    [tex]\frac{1}{z} = \frac{1}{r}*(cos\oslash-isin\oslash)[/tex]

    have no idea whats going on there lol.


    hope you can help :D
     
  2. jcsd
  3. Jul 3, 2007 #2

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    This is just using the double angle formula for sine: sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
    Expand the denominator, and use the identity sin^2x+cos^2x=1
     
  4. Jul 3, 2007 #3
    thnx buddy :D
     
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