UPSC NDA Math Model Paper 5

Given equation is: |z + 1| = |z – 1|
Let the value of ‘z’ be: z = x + iy
Now, the equation becomes,
⇒ |(x + iy) + 1| = |(x + iy)-1|
⇒ |(x + 1) + iy| = |(x – 1) + iy|
On taking modulus on both sides,
⇒√(x+1)2+y2=√(x−1)2+y2
⇒√x2+2x+1+y2=√x2−2x+1+y2
On squaring on both sides, we get
⇒x2+2x+1+y2=x2−2x+1+y2
⇒4x=0
∴x=0
Therefore, the equation represents y-axis.