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Math Help - [SOLVED] Roots in Polar Form

  1. #1
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    [SOLVED] Roots in Polar Form

    Hi

    If I am calculating roots in polar form how should I be displaying them?

    eg. The seventh roots of -128 are:

    z_{0} = \langle2,\pi/7\rangle
    z_{1} = \langle2,3\pi/7\rangle
    z_{2} = \langle2,5\pi/7\rangle
    z_{3} = \langle2,\pi\rangle = -2
    z_{4} = \langle2,9\pi/7\rangle
    z_{5} = \langle2,11\pi/7\rangle
    z_{6} = \langle2,13\pi/7\rangle

    Do I need to be displaying them like this?

    z_{0} = \langle2,\pi/7\rangle = 2(cos(\pi/7)+isin(\pi/7))

    etc, etc...

    Or like in the first example

    The reason I ask is because i'm asked to show how they make 3 complex conjugate pairs which I can see are

    z_{0} and z_{6}
    z_{1} and z_{5}
    z_{2} and z_{4}


    Thanks
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  2. #2
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    Quote Originally Posted by Ian1779 View Post
    eg. The seventh roots of -128 are:
    z_{0} = \langle2,\pi/7\rangle
    z_{1} = \langle2,3\pi/7\rangle
    z_{2} = \langle2,5\pi/7\rangle
    z_{3} = \langle2,\pi\rangle = -2
    z_{4} = \langle2,9\pi/7\rangle
    z_{5} = \langle2,11\pi/7\rangle
    z_{6} = \langle2,13\pi/7\rangle

    Do I need to be displaying them like this?

    z_{0} = \langle2,\pi/7\rangle = 2(cos(\pi/7)+isin(\pi/7))
    I think that really up to your instructor/textbook

    The reason I ask is because i'm asked to show how they make 3 complex conjugate pairs which I can see are
    z_{0} and z_{6}
    z_{1} and z_{5}
    z_{2} and z_{4}
    As to the complex conjugate pairs, take note.
    \arg (z) =  - \arg \left( {\overline z } \right)
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  3. #3
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    Thanks for the explanation about the arg!!

    Another reason I ask is that the follow on question asks me to factorise the polynomial x^7+128

    I've worked out that one of the roots are 2(cos(\pi/7)+isin(\pi/7)) and another is -2 hence my question about the polar forms as I feel i'm duplicating my work

    Any advice would be great

    Thanks
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  4. #4
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    Quote Originally Posted by Ian1779 View Post
    Another reason I ask is that the follow on question asks me to factorise the polynomial x^7+128
    x^7+128=(x-z_0)(x-z_1)(x-z_2)(x-z_3)(x-z_4)(x-z_5)(x-z_6)
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