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    On FP3 now, but have an upcoming mock. Please, can someone explain this to me? I used to like complex numbers until these transformation questions came up!
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    Many thanks.
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    Well, what's the general form of a point on the line Im z = 1/2?

    And then, what is the image of such a point under the transformation w = (z - i ) / z?

    The 2nd part is then a matter of scaling + translating the image of w to get what's described in the Q.
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    (Original post by DFranklin)
    Well, what's the general form of a point on the line Im z = 1/2?

    And then, what is the image of such a point under the transformation w = (z - i ) / z?

    The 2nd part is then a matter of scaling + translating the image of w to get what's described in the Q.
    z = x + 1/2i? Since only the imaginary part is constant?
    Then rearrange for w to get z = i/1-W, "realise" the denominator after letting w = u + iv. Eventually this yields u^2 + v^2 = 1, so mod(w) = 1. This makes sense to me, if correct?

    Part b though...
    Do I treat it as W = mod(z - (3+i)) = 2?
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    [QUOTE=AlphaArgonian;69591166]z = x + 1/2i? Since only the imaginary part is constant?
    Then rearrange for w to get z = i/1-W, "realise" the denominator after letting w = u + iv. Eventually this yields u^2 + v^2 = 1, so mod(w) = 1. This makes sense to me, if correct?[quote]Obviously I can't check details you haven't posted, but that all looks right.

    Part b though...
    Do I treat it as W = mod(z - (3+i)) = 2?
    I'd just think about it geometrically.

    i.e. OK, I've got a circle radius 1 around the origin. So I can get a circle of size 2 by mulitplying w by 2. (i.e. 2w is going to trace a circle radius 2 around the origin).

    Then I need to translate that circle so it's centered around 3+i. What do I need to do to 2w to do that?
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    (Original post by DFranklin)

    I'd just think about it geometrically.

    i.e. OK, I've got a circle radius 1 around the origin. So I can get a circle of size 2 by mulitplying w by 2. (i.e. 2w is going to trace a circle radius 2 around the origin).

    Then I need to translate that circle so it's centered around 3+i. What do I need to do to 2w to do that?
    Ok, that does clear things up, will definitely use this method.
    Many thanks.
 
 
 
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