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leaving cert complex numbers hl

  • 12-02-2015 12:00AM
    #1
    mayogirlie1
    Registered Users, Registered Users 2 Posts: 68 ✭✭


    Anyone please help quickly with 2nd part! :)


Comments

  • #2
    TheBody
    Registered Users, Registered Users 2 Posts: 5,657 ✭✭✭TheBody


    From the first part you should have [latex]z^2=-2-2\sqrt{3}i[/latex]

    If we sub the vaules for [latex]z^2[/latex] and [latex]z[/latex] into the statement in the second part we get:

    [latex]z^2+pz=(-2-2\sqrt{3}i)+p(-1+\sqrt{3}i)[/latex].

    When we multiply out the brackets and simplify we get:

    [latex]z^2+pz=(-2-p)+i(-2\sqrt{3}+p\sqrt{3})[/latex].

    As we want this to be a real number, that means we want the complex part to be zero. So we just need to let:

    [latex]-2\sqrt{3}+p\sqrt{3}=0[/latex]

    Solving for [latex]p[/latex] you will get that [latex]p=2[/latex].

    I'll let you fill in the calculation details. If you are still having problems, let me know and I'll provide some more detail.

    Good luck!


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