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    i need help with the following problem:
    Find every z belonging to Complex, such that |z|=sqrt(5) and z^3-2z+16=3conj(z)
    conj(a+bi)=a-bi
    I multiplied by z on both sides of the equation, but didnt know how to go on from z^4-2z^2+16z=15.

    Any help would be much appreciated.
    Thank you, Paul.
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    (Original post by pbialos)
    i need help with the following problem:
    Find every z belonging to Complex, such that |z|=sqrt(5) and z^3-2z+16=3conj(z)
    conj(a+bi)=a-bi
    I multiplied by z on both sides of the equation, but didnt know how to go on from z^4-2z^2+16z=15.

    Any help would be much appreciated.
    Thank you, Paul.
    Note that 1 and -3 are roots of your quartic, so you can take out factors of z+3 and z-1 from it.

    Of course they don't satisfy |z| = rt(5) but the other two roots may do.
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    (Original post by RichE)
    Note that 1 and -3 are roots of your quartic, so you can take out factors of z+3 and z-1 from it.

    Of course they don't satisfy |z| = rt(5) but the other two roots may do.
    Many Thanks. I could finish the exercise.
 
 
 
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