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    Need help with 7b. Not too sure what to do. I did part a by completing the square but in guessing I use my answer to this part some how.
    Cheers
    http://m.imgur.com/6eU7OFZ
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    (Original post by Super199)
    Need help with 7b. Not too sure what to do. I did part a by completing the square but in guessing I use my answer to this part some how.
    Cheers
    http://m.imgur.com/6eU7OFZ
    Let u=z^2 then use your answer to the first part and back-substitute.
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    Make a substitution w=z^2.

    Solve how you normally would solve a quadratic to find w.

    Then use the w=z^2 to find z.
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    (Original post by poorform)
    Make a substitution w=z^2.

    Solve how you normally would solve a quadratic to find w.

    Then use the w=z^2 to find z.
    (Original post by Zacken)
    Let u=z^2 then use your answer to the first part and back-substitute.
    But dont you just go back to the same quadratic as before.
    -3+4i =z^2
    -3-4i=z^2

    Sqaure roots of those give me the other roots? I cant remember how you do that
    Is this when you do (a+bi)^2=-3+4i
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    (Original post by Super199)
    But dont you just go back to the same quadratic as before.
    -3+4i =z^2
    -3-4i=z^2

    Sqaure roots of those give me the other roots? I cant remember how you do that
    Yes, that's the entire point. So now your rotos are given by z = \pm \sqrt{-3 + 4i}, \pm \sqrt{-3-4i}. You might want to quickly good how to find the square root of a complex number. Have you learnt De Moivre's theorem?
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    (Original post by Zacken)
    Yes, that's the entire point. So now your rotos are given by z = \pm \sqrt{-3 + 4i}, \pm \sqrt{-3-4i}. You might want to quickly good how to find the square root of a complex number. Have you learnt De Moivre's theorem?
    Yh sort of but does that involve putting it into cos theta+isin theta form?
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    (Original post by Super199)
    Yh sort of but does that involve putting it into cos theta+isin theta form?
    Yeah.
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    (Original post by Zacken)
    Yeah.
    Yh sorted cheers
    How do I do part d?
    |z-z1| <2 isnt that a circle i cant remember tbh.
    And the angle of z1 lies between 0 and pi/2?
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    (Original post by Super199)
    Yh sorted cheers
    How do I do part d?
    |z-z1| <2 isnt that a circle i cant remember tbh.
    And the angle of z1 lies between 0 and pi/2?
    |z-z_1| < 2 is the inside of a circle centred around z_1 with radius 2. The angle of z_1 lying between 0 and pi/2 just lets you know which root to pick as only one of the roots will be in the first quadrant and that is z_1.
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    (Original post by Zacken)
    |z-z_1| < 2 is the inside of a circle centred around z_1 with radius 2. The angle of z_1 lying between 0 and pi/2 just lets you know which root to pick as only one of the roots will be in the first quadrant and that is z_1.
    Yh got it cheers
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    (Original post by Super199)
    Yh got it cheers
    Good work!
 
 
 
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