IIT JEE , AIEEE Forum - Mathematics , Algebra

aratrika

THE EXPRESSION GIVEN:

|z| -2 = |z-i|- |z +5i | = 0

so, |z| -2 = 0

x^2 + y^2 -2 = 0

or, x^2 + y^2 =2 ......[1]

again ,

|x+ iy - i| - |x+iy+5i| =0

or, |x + i(y-1)| - |x + i(y+5)| = 0

or, x^2 + y^2 +1 - 2y = x^2 + y^2 + 25 + 10y

[substituting the value of (x^2 + y^2) = 2]

2 + 1 - 2y = 2+ 25 + 10y

or, -12y= 24

or, y= -2

now substituting the value of y from above eqn. in [1], we get,

x^2 + (-2)^2 = 2

or ,x^2 = -2

^{OR, x =2 ^1/2 i}

since real part cant be imaginary, hence x=0

so, it gives single point i.e(0, -2)

ans: c)

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