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Math Help - Complex numbers! Elementary problem *Quick help needed*

  1. #1
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    Complex numbers! Elementary problem *Quick help needed*

    So im stuck at;
    Find the complex numbers with abs 1 for which it works that:
    |1-zi|=1

    How do I solve it? I've tried almost everything I can use and do, the problem is I don't know where to start.

    I've tried setting
    z=a+bi
    |1-zi|=1 as z(roof)
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  2. #2
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    This is the same as |(1+y)-xi|=1 or (1+y)^2+x^2=1.
    That is a circle of points in the complex plane with center -i with radius 1.
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  3. #3
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    Yeah I tried it, and it does not work. Well atleast it's not the same as the answer im supposed to get which is;

    (+-)sqr(3)/2 - i/2

    I understand exactly how you think, thought for me it's the Z part of |1-zi|=1 which ruins every and all attempts for me to crack this problem.
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  4. #4
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    Well if you want the abolute value to be 1, solve these two.
    (1+y)^2+x^2=1 & x^2+y^2=1.
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