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If z = x + iy is a complex number such t...

If z = x + iy is a complex number such that `|(z-4i)/(z+ 4i)|` = 1 show that the locus of z is real axis.

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Knowledge Check

  • If z = x + iy is a complex number such that |z + 2| = |z - 2|, then the locus of z is

    A
    real axis
    B
    imaginary axis
    C
    ellipse
    D
    circle

  • If |(z-i)/(z+i)|=1 , then the locus of z is

    A
    `x=0`
    B
    `y=0`
    C
    `x=1`
    D
    `y=1`

  • If z= x + iy is a complex number such that |z+2|=|z-2| , then the locus of z is

    A
    real axis
    B
    imaginary axis
    C
    ellipse
    D
    circle

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