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Math Help - complex problem

  1. #1
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    complex problem

    show that the equation of the tangent to the circle mod(z)=r where r>0 at point z0 is given by ((conjugate) (z0))*z+z0*((conjugate)(z)=2*r^2


    not understanding how to do this as moving point on the circumference of circle is z but what is z0
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by prasum View Post
    show that the equation of the tangent to the circle mod(z)=r where r>0 at point z0 is given by ((conjugate) (z0))*z+z0*((conjugate)(z)=2*r^2


    not understanding how to do this as moving point on the circumference of circle is z but what is z0

    $$ z_0 is a given point on the circle and $$ z is an arbitrary point on the tangent.

    CB
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  3. #3
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    can yu please help me solve the problem

    do we have to use concept of rotation in it
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by prasum View Post
    can yu please help me solve the problem

    do we have to use concept of rotation in it
    The reason I have not attempted to solve this is because I do not know how you are expected to solve it, and suspect how I would approach this is not acceptable for you to submit.

    You could start by writing it in cartesians so z=x+i y, and z_0=r (\cos(\theta)+i \sin(\theta)), then plug these into the proposed equation and show that it is a straight line which passes through  z_0 and has gradient -1/\tan(\theta)

    CB
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  5. #5
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    can yu please elaborate yur solution
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