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How to change complex numbers from polar to cartesian form? Watch

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    I have some complex number answers. I need to chnage them from polar form('modulus' < 'Argument') to Cartesian form(2+1j).
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    (Original post by MatthewTG)
    I have some complex number answers. I need to chnage them from polar form('modulus' < 'Argument' to Cartesian form(2+1j).
    You know that re^{i \theta} = r(\cos \theta + i \sin \theta) = z so, uh, that's pretty much it.

    For example 2e^{i \frac{\pi}{4}} = 2(\cos \frac{\pi}{4} + i \sin \frac{\pi}{4}) = 2(\frac{1}{\sqrt{2}} + \frac{i}{\sqrt{2}})
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    (Original post by Zacken)
    You know that re^{i \theta} = r(\cos \theta + i \sin \theta) = z so, uh, that's pretty much it.

    For example 2e^{i \frac{\pi}{4}} = 2(\cos \frac{\pi}{4} + i \sin \frac{\pi}{4}) = 2(\frac{1}{\sqrt{2}} + \frac{i}{\sqrt{2}})
    can you walk through it in baby steps?
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    (Original post by MatthewTG)
    can you walk through it in baby steps?
    Are you doing FP1 or FP2?
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    (Original post by MatthewTG)
    can you walk through it in baby steps?
    Sorry, I'm not sure how much more simpler I can possibly make it... could you perchance tell me which bit do you not understand? Are you unfamiliar with the cos + i sin form?
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    (Original post by MatthewTG)
    I have some complex number answers. I need to change them from polar form('modulus' < 'Argument' to Cartesian form(2+1j).
    Complex numbers of the form z = a+bj can be expressed in the form z=r(cos\theta +jsin\theta), where r=|z| and \theta = arg(z), it can be shown from Pythagoras' theorem. So just find the modulus and argument of the complex number 2+j and you can express it in polar form.
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    (Original post by NotNotBatman)
    Complex numbers of the form z = a+bj can be expressed in the form z=r(cos\theta +jsin\theta), where r=|z| and \theta = arg(z), it can be shown from Pythagoras' theorem. So just find the modulus and argument of the complex number 2+j and you can express it in polar form.
    My numbers are:
    1.0586 + 0.1677i
    0.1677 + 1.0586i
    0.4866 - 0.9550i
    -0.7579 - 0.7579i
    -0.9550 + 0.4866i

    Please tell me how to change them from cartesian to polar form
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    (Original post by MatthewTG)
    My numbers are:
    1.0586 + 0.1677i
    0.1677 + 1.0586i
    0.4866 - 0.9550i
    -0.7579 - 0.7579i
    -0.9550 + 0.4866i

    Please tell me how to change them from cartesian to polar form
    Assume your complex numbers are in the form:
    x + yi

    Compute:
    Modulus = Root(x^2+y^2) = R
    Arg = Tan^-1(y/x) (Tan^-1 for arctan/tan inverse)

    Then put it in the form R((cos(arg)+isin(arg))
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    (Original post by Hayytch)
    Assume your complex numbers are in the form:
    x + yi

    Compute:
    Modulus = Root(x^2+y^2) = R
    Arg = Tan^-1(y/x) (Tan^-1 for arctan/tan inverse)

    Then put it in the form R((cos(arg)+isin(arg))
    Note that because arctan(x/y) = arctan(-x/-y), you need to be aware of what quadrant your point lies in and potentially adjust by +/- pi.

    E.g. -1-i gives x=y=-1 and so arctan(x/y) = pi/4 but the argument you actually want is -3pi/4.

    Just in case the OP is doing this on a computer: many programmer/languages have a special function that returns the correct argumentt - often it's atan2(x, y).

    Most calculators also do rectangular to polar conversion, or at least they did in my day.
 
 
 
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