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Math Help - complex plane

  1. #1
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    complex plane

    hi guys

    x + yi = cos(theta) + i sin(theta)

    I understand this formula quite quite well...

    But I have problem to think/understand how come if I have cos(theta) + i sin(theta) given I can come up with the x+yi form

    Think in this way:

    If someone gave me this input

    cos(theta) + i sin(theta) == cos(0.6) + i sin(0.8) % in rad - and ask me to find x+yi version of this...

    E.g. they look for x + yi , this is equal with 3 + 4i

    How come I can come to this kind of conclusion? ...
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  2. #2
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    Quote Originally Posted by problady View Post
    If someone gave me this input
    cos(theta) + i sin(theta) == cos(0.6) + i sin(0.8) % in rad - and ask me to find x+yi version of this...
    E.g. they look for x + yi , this is equal with 3 + 4i
    How come I can come to this kind of conclusion? ...
    \cos(0.6) + \mathbf{i} \sin(0.8) is in the x +y \mathbf{i} form.
    You see x=\cos(0.8)~\&~y=\sin(0.8).
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  3. #3
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    NO NO NO ... I am asking how to get x=3 y=4 ? ... that what you say is quite easy, right?
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  4. #4
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    Quote Originally Posted by problady View Post
    NO NO NO ... I am asking how to get x=3 y=4 ? ... that what you say is quite easy, right?
    I have absolutely no idea what that means.

    Given 3+4\mathbf{i} let \theta  = \arctan \left( {\frac{4}{3}} \right).

    Then 3+4\mathbf{i}=5\cos(\theta)+5\mathbf{i}\sin(\theta  ).
    Is that what it means?
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  5. #5
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    Please read my first post, I think is quite well explained!

    Based on maths we know this formula: x + yi = cos(theta) + i sin(theta)

    Now think in this way, someone has given you the right-hand side e.g., cos(0.6) + i sin(0.8)

    And is asking you to find the left-hand side, which in this case is 3 + 4i

    But as you may guess, could be: 6 + 8i, 12 + 16i etc. as well

    So my question is given the right-hand side can we find left-hand side? Since given left-hand side we can find right-hand side precisely!
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  6. #6
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    Quote Originally Posted by problady View Post
    Please read my first post, I think is quite well explained!
    Based on maths we know this formula: x + yi = cos(theta) + i sin(theta)
    Now think in this way, someone has given you the right-hand side e.g., cos(0.6) + i sin(0.8)
    And is asking you to find the left-hand side, which in this case is 3 + 4i
    But as you may guess, could be: 6 + 8i, 12 + 16i etc. as well
    So my question is given the right-hand side can we find left-hand side? Since given left-hand side we can find right-hand side precisely!
    Your got to be joking! Are you not?

    Post an exact problem.
    Last edited by Plato; April 4th 2011 at 11:55 AM.
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  7. #7
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    "Based on maths we know this formula: x + yi = cos(theta) + i sin(theta)" This is not correct, z=x+iy=\sqrt{x^2+y^2}(\cos \theta+i\sin \theta) (trigonometrical form)

    So x=\sqrt{x^2+y^2}\cos \theta and y=\sqrt{x^2+y^2}\sin \theta. (I hope you know that \sqrt{x^2+y^2}=|z|)

    For your example: (which is wrong/ not complete)
    1. False. cos(0.6) + i sin(0.8)=cos(theta) + i sin(theta) Try to guess what is wrong here! ^^
    2. z=3 + 4i=x+iy (x=3, y=4)
    |z|=\sqrt{3^2+4^2}=\sqrt{25}=5
    \cos \theta = \frac{x}{|z|}=\frac{3}{5}
    \sin \theta = \frac {y}{|z|}=\frac{4}{5}

    You have some serious problems with theory. Learn it! >.<
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  8. #8
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    No I am not joking ... I am learning maths without a teacher thats right!

    So, given this:
    x + yi = cos(0.6) + i sin(0.8)

    What is the value of x+yi - 3 + 4i, 6 + 8i or 12 + 16i - is possible to decide for one of those?
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  9. #9
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    z=x+iy=\sqrt{x^2+y^2}(\cos \theta+i\sin \theta) (trigonometrical form)

    I had incomplete formula Plato sorry! This formula helps me to understand my way... no everything is clear!

    Thanks to you Plato bot more to veileen
    Last edited by problady; April 4th 2011 at 12:08 PM.
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