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Math Help - Complex no.

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    Complex no.

    If Z_{1},Z_{2} and Z_{3} are Complex no. Representing The Vertices of a Triangle inscribed in |Z|=2. The

    Altitude Through Z_{1} meets the Circumcircle in P, Then The Complex no. Corrosponding To P is =

    (Ans in Terms of Z_{1},Z_{2} and Z_{3})
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    Quote Originally Posted by jacks View Post
    If Z_{1},Z_{2} and Z_{3} are Complex no. Representing The Vertices of a Triangle inscribed in |Z|=2. The

    Altitude Through Z_{1} meets the Circumcircle in P, Then The Complex no. Corrosponding To P is =

    (Ans in Terms of Z_{1},Z_{2} and Z_{3})
    Dear jacks,

    Let, z_1=x_1+iy_1

    z_2=x_2+iy_2

    z_3=x_3+iy_3

    Then write the gradient of the Z_{2}Z_{3} line. Let it be m_1.

    Since Z_{2}Z_{3} and PZ_{1} are perpendicular you could find the gradient of the PZ_{1} line by,

    m_{1}\times m=-1

    Then you could fine the equation of the PZ_{1} line. Hint: You know the gradient and a point on the PZ_{1} line. Let the equation be y=mx+c----(1)

    The equation of the circle could be written as, \mid Z\mid=2\Rightarrow{x^2+y^2=4}-----------(2)

    Using equations (1) and (2) you can find the point P.
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