If z = x+iy, then the equation |z+1| = |z-1| represents

Question

If z = x+iy, then the equation |z+1| = |z-1| represents (A) a circle (B) a parabola (C) x-axis (D) y-axis

Tardigrade Admin · Accepted Answer

|z+1|=|z-1| Let z=x+i y Then, |x+i y+1|=|x+i y-1| ⇒ √(x+1)2+y2=√(x-1)2+y2 ⇒ (x+1)2+y2=(x-1)2+y2 ⇒ x2+2 x+1+y2=x2+1-2 x+y2 ⇒ 4 x=0 ⇒ x=0 which represents y- axis.

Q. If z = x+iy, then the equation |z+1| = |z-1| represents

a circle

a parabola

x-axis

y-axis

∣z+1∣=∣z−1∣ Let z=x+iy Then, ∣x+iy+1∣=∣x+iy−1∣ ⇒(x+1)2+y2​=(x−1)2+y2​ ⇒(x+1)2+y2=(x−1)2+y2 ⇒x2+2x+1+y2=x2+1−2x+y2 ⇒4x=0 ⇒x=0 which represents y− axis.