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    Vi Nguyen's Avatar
    Vi Nguyen Posts: 48, Reputation: 2
    Junior Member
     
    #1

    Jul 3, 2009, 04:43 AM
    roots of polynomials
    Need to find the roots of :

    1) ( z^4)+(4z^2)+16=0

    2) (z+i)^5-(z-i)^5=0

    thanks :)
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #2

    Jul 3, 2009, 09:26 AM

    Well, I've not done complex no.s yet, but consulting my book, I think you can get it that way;

    1)










    So,



    Then you simplify. Note that I'm not sure if that's how it is done, I'm trying.
    Vi Nguyen's Avatar
    Vi Nguyen Posts: 48, Reputation: 2
    Junior Member
     
    #3

    Jul 4, 2009, 10:57 AM
    roots of polynomials
    Can someone show me how to find the roots of:
    (Z^4)+(Z^3)+(Z^2)+Z+1

    Please show how you worked this out. Thanks
    Vi Nguyen's Avatar
    Vi Nguyen Posts: 48, Reputation: 2
    Junior Member
     
    #4

    Jul 4, 2009, 11:01 AM
    This isn't the answer given in my book. The answer given is
    plus or minus one plus or minus i root three. Thanks for trying but, spinning me out too :)

    Quote Originally Posted by Unknown008 View Post
    Well, I've not done complex no.s yet, but consulting my book, I think you can get it that way;

    1)










    So,



    Then you simplify. Note that I'm not sure if that's how it is done, I'm trying.
    Vi Nguyen's Avatar
    Vi Nguyen Posts: 48, Reputation: 2
    Junior Member
     
    #5

    Jul 4, 2009, 11:11 AM
    roots of complex no.s
    Can someone show the workings to finding the roots of:

    (Z+i)^5 - (Z-i)^5=0

    Apparently it can be done using complex exponentials and roots of unity (whatever that means), anyway the answer is Z=√((52√5)/5)
    ScottGem's Avatar
    ScottGem Posts: 64,966, Reputation: 6056
    Computer Expert and Renaissance Man
     
    #6

    Jul 4, 2009, 12:02 PM

    Please review the guidelines on asking for help with homework that can be found here:



    Ask Me Help Desk - Announcements in Forum : Arts & Literature
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
     
    #7

    Jul 4, 2009, 03:18 PM
    Quote Originally Posted by Vi Nguyen View Post
    Can someone show me how to find the roots of:
    (Z^4)+(Z^3)+(Z^2)+Z+1

    Please show how you worked this out. Thanks

    Rewrite as:



    Now, use the quadratic formula on each of those and find the 4 roots. All 4 are complex.
    Vi Nguyen's Avatar
    Vi Nguyen Posts: 48, Reputation: 2
    Junior Member
     
    #8

    Jul 5, 2009, 01:13 AM
    If you haven't noticed it's the end of semester break, so this isn't for homework, just asking these questions to tie up loose ends.

    Quote Originally Posted by ScottGem View Post
    Please review the guidelines on asking for help with homework that can be found here:



    Ask Me Help Desk - Announcements in Forum : Arts & Literature
    ScottGem's Avatar
    ScottGem Posts: 64,966, Reputation: 6056
    Computer Expert and Renaissance Man
     
    #9

    Jul 5, 2009, 05:20 AM

    Quote Originally Posted by Vi Nguyen View Post
    If you haven't noticed it's the end of semester break, so this isn't for homework, just asking these questions to tie up loose ends.
    If you haven't noticed, schools have different semesters all over the world. Since you don't list your location, I have no idea what your school schedule is.

    But that is not the issue. I've reviewed several of your threads, in all those threads, you post a problem and ask someone to solve it for you. You show no effort to do the work yourself. And that violates the rules of this site. Any further attempts on your part to get people to do your work for you will be removed.
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
    Ultra Member
     
    #10

    Jul 5, 2009, 08:09 AM
    Quote Originally Posted by Vi Nguyen View Post
    Can someone show the workings to finding the roots of:

    (Z+i)^5 - (Z-i)^5=0

    Apparently it can be done using complex exponentials and roots of unity (whatever that means), anyway the answer is Z=√((52√5)/5)
    Did you try factoring?


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