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Math Help - Complex Numbers, Polar Coordinates

  1. #1
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    Complex Numbers, Polar Coordinates

    Okay, I have this so far

    z= -1+7i

    As far as what I have for polar coordinate equation, this is it:

    z= 6.93(cos180+ i sin?)

    My problem is that 7 cannot be converted into an angle.

    What would I do for this?
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  2. #2
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    Quote Originally Posted by jschlarb View Post
    Okay, I have this so far

    z= -1+7i

    As far as what I have for polar coordinate equation, this is it:

    z= 6.93(cos180+ i sin?)

    My problem is that 7 cannot be converted into an angle.

    What would I do for this?
    Please show >all< of your working ..... Then it will be much easier to explain your mistakes to you ....
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  3. #3
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    z=-1+7i

    a=-1, b=7, r= [square root] a^2+b^2 = 6.93 (subbed in -1 and 7)

    cos^-1 (-1) = 180, sin^-1 (7) = does not exist

    z=6.93(cos180+ i sin ?)

    You'll have to forgive me, I'm not sure of the tag for square roots (if there is a link to all math signs, could you please link it?)
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  4. #4
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    Quote Originally Posted by jschlarb View Post
    z= -1+7i or polar coordinates
    First just do the basic computations: \theta  = \arg \left( { - 1 + 7i} \right) = \arctan \left( {\frac{7}{{ - 1}}} \right) + \pi \,\& \,\sqrt {\left( { - 1} \right)^2  + 7^2 }  = 5\sqrt 2 .
    Now z = 5\sqrt 2 e^{i\theta } .
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  5. #5
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    Quote Originally Posted by jschlarb View Post
    z=-1+7i

    a=-1, b=7, r= [square root] a^2+b^2 = 6.93 (subbed in -1 and 7)

    cos^-1 (-1) = 180, sin^-1 (7) = does not exist

    z=6.93(cos180+ i sin ?)

    You'll have to forgive me, I'm not sure of the tag for square roots (if there is a link to all math signs, could you please link it?)
    You should know that the argument of z = a + ib is \theta = \tan^{-1} \frac{b}{a} where you have to be careful what quadrant (and hence value) you choose for \theta ..... A simple argand diagram showing z = a + ib will help you make that decision.

    For the question you've posted, \theta = \tan^{-1} \frac{7}{-1} = \tan^{-1} (-7).

    An argand diagram easily shows that z = -1 + 7i lies in the 2nd quadrant, so \theta = \tan^{-1} (-7) + \pi \approx  -1.429 +  \pi = 1.713 radians.

    Therefore z = -1 + 7i = r (\cos \theta + i \sin \theta) = .....
    Last edited by mr fantastic; June 22nd 2008 at 04:25 PM. Reason: Corrected a few typos
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