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The complex numbers z is simultaneously ...

The complex numbers z is simultaneously satisfy the equations `abs(z-12)/abs(z-8i)=5/3,abs(z-4)/abs(z-8)=1` then the Re(z) is

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The complex number z satisfying the equation |z-i|=|z+1|=1 is

If the complex number z satisfies the equations |z-12|/|z-8i|=(5)/(3) and |z-4|/|z-8| =1, "find" z.

Knowledge Check

  • The locus represented by the equation abs(z-1)=abs(z-i) is

    A
    a circle of radius 1
    B
    an ellipse with foci 1 and (-1)
    C
    a line through the origin
    D
    a circle on the line joining 1 and (-1) as diameter

  • The complex number z satisfying the question |(i -z)/(i+z)|=1 lies on-

    A
    a circle with the centre `(0,0)` and radius 1
    B
    the x-axis
    C
    the y-axis
    D
    the line `y=x+1`

  • If absz=min{abs(z-1), abs(z+1)} , then

    A
    `abs(z+barz)=1/2`
    B
    `z+barz=1`
    C
    `abs(z+barz)=1`
    D
    None of these

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