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Solution :

Let z = x + iy <br> Given that, `|(z-5i)/(z+5i)|=|(x+iy-5i)/(x+iy+5i)|` <br> `|(z-5i)/(z+5i)|=|(x+i(y-5i))/(x+i(y+5i))|" "[:'|(z-5i)/(z+5i)|=1]` <br> <br> `rArr |(z-5i)/(z+5i)|=|sqrt(x+i(y-5i))/(sqrtx+i(y+5i))|` <br> On squaring both sides, we get <br> `x^(2)+(y-5)^(2)+(y+5)^(2)` <br> `rArr `-10y=+10y` <br> `rArr 20 = 0` <br> `:. y+0` <br> So, z lies on real axis .