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Math Help - Finding roots of complex number

  1. #1
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    Post Finding roots of complex number

    Find the fourth roots of 8√ 3 + 8i.
    Graph each root on complex plane.

    I think I have the roots...am I correct?
    I don't understand how to graph them.

    z1 = 4V16(cosπ/24 + isin π/24)

    z2 = 4V16(cos 13π/24 + isin 13π/24)

    z3 = 4V16(cos 25/24 + isin 25π/24)

    z4 = 4V16(cos 37π/24 + isin 37π/24)

    Do I have to change these to complex numbers to graph? How would I do that?

    Thanks!
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  2. #2
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    Here is the graph.
    Attached Thumbnails Attached Thumbnails Finding roots of complex number-cplx.gif  
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    ok...so were my answers correct?

    Would root 1 be 1.402 + 0.19i ?

    How did you come up with the points on the graph?

    thanks!
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    Quote Originally Posted by live_laugh_luv27 View Post
    ok...so were my answers correct?
    Would root 1 be 1.402 + 0.19i ?
    How did you come up with the points on the graph?
    It is a program for classroom demonstrations that I wrote eight or so years using the CAS MathCad. I can input a complex number and each change in the index the graph will update.
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  5. #5
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    Quote Originally Posted by live_laugh_luv27 View Post
    Find the fourth roots of 8√ 3 + 8i.
    Graph each root on complex plane.

    I think I have the roots...am I correct?
    I don't understand how to graph them.

    z1 = 4V16(cosπ/24 + isin π/24)

    z2 = 4V16(cos 13π/24 + isin 13π/24)

    z3 = 4V16(cos 25/24 + isin 25π/24)

    z4 = 4V16(cos 37π/24 + isin 37π/24)

    Do I have to change these to complex numbers to graph? How would I do that?

    Thanks!
    Assuming you mean that "4V16" is the 4th root of 16, you might as well replace them with "2."

    You don't have to change the complex numbers to standard (a + bi) form if you know polar coordinates. They are in the form of P(r, θ), where r is the directed distance from the origin to P, and θ is the directed angle whose initial side is on the polar axis (which corresponds to the positive x-axis) and whose terminal side is on the line OP. So you would plot the points (2, π/24), (2, 13π/24), (2, 25π/24), and (2, 37π/24), which is what Plato did.


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