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where does z lie , if |(z-5i)/(z+5i)|=1?...

where does z lie , if `|(z-5i)/(z+5i)|=1?`

Text Solution

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Let z = x + iy
Given that, `|(z-5i)/(z+5i)|=|(x+iy-5i)/(x+iy+5i)|`
`|(z-5i)/(z+5i)|=|(x+i(y-5i))/(x+i(y+5i))|" "[:'|(z-5i)/(z+5i)|=1]`

`rArr |(z-5i)/(z+5i)|=|sqrt(x+i(y-5i))/(sqrtx+i(y+5i))|`
On squaring both sides, we get
`x^(2)+(y-5)^(2)+(y+5)^(2)`
`rArr `-10y=+10y`
`rArr 20 = 0`
`:. y+0`
So, z lies on real axis .
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Knowledge Check

  • The complex numbers z = x + iy which satisfy the equation |( z - 5i)/( z + 5i)| = 1 lie on

    A
    the x-axis
    B
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    A
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    B
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