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complex numbers watch

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    a = 1 +4j
    a^2 = 8j - 15
    a^3 = -52j - 47

    a satisfies

    z^3 + 5z^2 +kz +m = 0

    find k and show m = 119

    ive dun questions like this before but just forgot how to go about it - thanx

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    i think i got it by comparing coefficients

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    so dont worry bout it - thanx
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    they then ask for the 2 other roots of the equation. So there is the conjugate 1-4j and i got -7 as the other root. it then asks for their arguments and i got 0 for -7 and +/- 1.33 for the other two roots respectively.

    the next part is :

    verify that there is a constant c such that all three roots satisfy |z+2| = c

    draw an argand diagram showing the locus of points representing all complex numbers z for which |z+2| = c.

    ne idea?
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    c = 5, which you can see by plugging the roots into |z + 2|.

    |z + 2| = 5 is a circle with its center at (-2, 0) and radius 5.
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    as dvs says...I was just about to write the same sort of thing
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    (Original post by dvs)
    c = 5, which you can see by plugging the roots into |z + 2|.

    |z + 2| = 5 is a circle with its center at (-2, 0) and radius 5.
    cool thanx - but how did u no the centre?

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    its ok i see now
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    For a specific locus, |z-(a+bj)| = r, this is the same as saying 'where can the points of z lie, such that a vector from (a+bj) to z has a distance r.
 
 
 
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