Question

Show that the complex number z = x + iy which satisfies the equation |z -5i/z +5i| = 1  lies on the x-axis.

Answer 1

|Z-5i/Z +5i|

Z = x + iy

⇒|x + i(y – 5)| = |x + i(y+5)|

⇒x² + (y – 5)² = x² + (y + 5)²

⇒y = 0

i.e. complex part of Z is zero. 

Z is pure real i.e. it lies on x axis.