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Math Help - Principle value of argument

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    Principle value of argument

    How do I find the principle value of the argument of ?
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    Quote Originally Posted by RossLeeds View Post
    How do I find the principle value of the argument of ?
    Principal (note spelling) value of the argument of what?
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    Quote Originally Posted by Opalg View Post
    Principal (note spelling) value of the argument of what?
    Sorry, confusion with the image - the princiPAL value of the argument of:

    exp( 7 + 4i )
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    Quote Originally Posted by RossLeeds View Post
    Sorry, confusion with the image - the princiPAL value of the argument of:

    exp( 7 + 4i )
    e^{7 + 4i} = e^7 e^{4i}

    So the argument is 4 radians. Therefore the principal argument is ....?
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    Quote Originally Posted by mr fantastic View Post
    e^{7 + 4i} = e^7 e^{4i}

    So the argument is 4 radians. Therefore the principal argument is ....?
    arctan 4?
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    Quote Originally Posted by RossLeeds View Post
    arctan 4?
    No. The argument is an angle (in this case, 4 radians). But an angle is only determined up to a multiple of 2π. The principal value of the argument is obtained by taking the value of the argument that lies in some specified interval of length 2π, usually the interval (-\pi,\pi]. So if 4 lies in that interval then the principal value is just 4. Otherwise, you'll have to add or subtract a multiple of 2π to 4 in order to bring it into that interval.
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