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    Post complex no.

    Hey All,

    How would you find the following complex number problem:

    find the four roots of the equation z^4= j3, expressing yuor answer in the form re^{jθ}, where r and θ are real. sketch their positions in an Argand diagram.

    Thanks
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    Quote Originally Posted by dadon View Post
    Hey All,

    How would you find the following complex number problem:

    find the four roots of the equation z^4= j3, expressing yuor answer in the form re^{jθ}, where r and θ are real. sketch their positions in an Argand diagram.

    Thanks
    But j3 you mean i^3 ?
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    well the question i copied it from is j3. unless their was a typo?

    buy don't complex numbers have the form a +jb
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    Quote Originally Posted by dadon View Post
    well the question i copied it from is j3. unless their was a typo?

    buy don't complex numbers have the form a +jb
    Typically most Mathematicians (and Physicists) use i^2 = -1. Engineers typically use j^2 = -1. Though, of course, there are exceptions to that rule.

    -Dan
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  5. #5
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    yes this is from an engineering book where j^2= -1

    How about this question instead?

    find the four roots of the equation z^4= -16, expressing your answer in the form a+jb, where a and b are real. sketch their positions in an Argand diagram.
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    Quote Originally Posted by dadon View Post
    Hey All,

    How would you find the following complex number problem:

    find the four roots of the equation z^4= j3, expressing yuor answer in the form re^{jθ}, where r and θ are real. sketch their positions in an Argand diagram.

    Thanks
    First you need to know or be able to derive:

    j = e^{pi j/2 + 2 pi j n}, n=0, +/-1, ...

    this is because: e^{pi j/2} = cos(pi/2) + j sin(pi/2) = j.

    Now z^4 = j^3 = e^{3 pi j/2 + 6 pi j n}, and so:

    z = e^{[3 pi j/2 + 6 pi j n]/4} = e^{3 pi j/8 + 3/2 pi j n},

    Putting n =0, 1, 2, 3 should give four distinct values for z, and any
    other value will again give one of these.

    RonL
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    Quote Originally Posted by dadon View Post
    find the four roots of the equation z^4= -16, expressing your answer in the form a+jb, where a and b are real. sketch their positions in an Argand diagram.
    Im still confused on this topic. how would u work out the quoted question.

    we need LaTex back!!
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