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    Hey Guys,
    I have a question with a Leaving cert maths question on complex Numbers.
    It is Q2 B (ii)
    here is the paper: http://www.examinations.ie/archive/e...03ALP130EV.pdf

    i have labeled in my points but don't know how to find the argument when they don't give values!
    an explanation would prove ever so helpful! thanks in advance.
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    (Original post by outnumbered)
    Hey Guys,
    I have a question with a Leaving cert maths question on complex Numbers.
    It is Q2 B (ii)
    here is the paper: http://www.examinations.ie/archive/e...03ALP130EV.pdf

    i have labeled in my points but don't know how to find the argument when they don't give values!
    an explanation would prove ever so helpful! thanks in advance.
    It's annoying that the question expects you to believe that the diagram is to scale without explicitly mentioning it anywhere but assuming that it is, what is arg(z^3)?
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    I know. this is the new type of maths the irish gouverment brought in. It has loads of fallacies.....
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    Anyone have an idea?
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    (Original post by outnumbered)
    Anyone have an idea?
    Hasn't Farhan's hint helped?

    Have you worked out which of the numbers is z, which is z^2 and which is z^3?

    Once you've done that, you can see which is z^3 and that will tell you what its argument is
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    To be honest, it hasn't.
    How would i work out what they are? Do i just do trial and error? i have figured out there positions on the argand diagram but after that i am lost....... sorry.
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    (Original post by outnumbered)
    To be honest, it hasn't.
    How would i work out what they are? Do i just do trial and error? i have figured out there positions on the argand diagram but after that i am lost....... sorry.
    You're told that z has modulus bigger than 1. Assuming (as seems reasonable) that the picture is to scale, then higher powers of z have bigger moduli. This tells you that z^3 is the point shown on the imaginary axis.

    I'm sure you know what the argument is of a point on the imaginary axis, so what possible arguments (when cubed) could take you to such a point?
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    Assuming you've done part i correctly, you're also given the quadrants of z^1, z^2 and z^3 and hence the bounds of the angle.

    Specifically:

    pi/2<Arg(z)<pi
    3pi/2<Arg(z^2)<2pi

    And, as davros mentioned

    Arg(z^3)=pi/2
 
 
 
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