|=1 ‌‌or ‌‌‌‌‌‌‌|z−6i|=|z+6i| Let ‌‌z=x+iy ‌‌ or ‌‌‌|x+iy−6i|=|x+iy+6i| ‌‌‌‌‌|x+(y−6)i|=|x+(y+6)i| ‌⇒√x2+(y−6)2=√x2+(y+6)2 ‌⇒‌‌x2+(y−6)2=x2+(y+6)2 ‌⇒y2+36−12y=y2+36+12y ‌⇒‌‌24y=0 ‌⇒‌‌y=0 Hence, it is lie on the real axis.