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    https://8dedc505ac3fba908c50836f5905...%20Edexcel.pdf

    Q12) How can z be transformed onto a full circle? The circle equation I get but doesn't it have to satisfy 0 < x < 1 and -1 < y < 0?
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    Zacken TeeEm
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    (Original post by TheFarmerLad)
    Zacken TeeEm
    Can you be more specific? I don't fully understand your question. Where does 0 < x < 1 and -1 < y < 0 come from?
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    (Original post by Zacken)
    Can you be more specific? I don't fully understand your question. Where does 0 < x < 1 and -1 < y < 0 come from?
    So instead of treating arg(z) = pi/4 as x + xi the MS suggested, I did it the argument way and got arg (1 - wi) - arg (w -1) = pi/4, which is a circle that satisfies mod w = 1, however only within the ranges I posted above. Surely the MS method is wrong as it treats arg (z) = pi/4 as x + xi, which is only true for values in the positive quadrant.. hope that makes more sense..?
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    (Original post by TheFarmerLad)
    So instead of treating arg(z) = pi/4 as x + xi the MS suggested, I did it the argument way and got arg (1 - wi) - arg (w -1) = pi/4, which is a circle that satisfies mod w = 1, however only within the ranges I posted above. Surely the MS method is wrong as it treats arg (z) = pi/4 as x + xi, which is only true for values in the positive quadrant.. hope that makes more sense..?
    But arg(z) = pi/4 is only values in the positive x and y quadrant. That's why it's called a half-line.

    Anyways, with your method, why does arg(1-wi) - arg(w-1) bring up the ranges that you specified?
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    (Original post by Zacken)
    But arg(z) = pi/4 is only values in the positive x and y quadrant. That's why it's called a half-line.

    Anyways, with your method, why does arg(1-wi) - arg(w-1) bring up the ranges that you specified?
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    Does that help?
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    (Original post by TheFarmerLad)
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    Does that help?
    Question doesn't say the image of the given half line is the circle, only that the image of the half line lies on the circle - this doesn't imply the entire circle.
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    (Original post by ghostwalker)
    Question doesn't say the image of the given half line is the circle, only that the image of the half line lies on the circle - this doesn't imply the entire circle.
    I realise that, but am I right in saying that the complex numbers on arg(z) = pi/4 can only be mapped onto those in the shaded region I previously specified?
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    (Original post by TheFarmerLad)
    I realise that, but am I right in saying that the complex numbers on arg(z) = pi/4 can only be mapped onto those in the shaded region I previously specified?
    Yes, it's just the lower right quadrant, but it's the part of the circle only, not any area.
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    (Original post by ghostwalker)
    Yes, it's just the lower right quadrant, but it's the part of the circle only, not any area.
    Thank you for your help
 
 
 
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