JEE WhatsApp Group
Sign in
Please select an account to continue using cracku.in
↓ →
JEE WhatsApp Group
Join Our JEE Preparation Group
Prep with like-minded aspirants; Get access to free daily tests and study material.
We need $$|z - i| = |z + i| = |z - 1|$$.
Let $$z = x + iy$$.
From $$|z - i| = |z + i|$$:
$$\sqrt{x^2 + (y-1)^2} = \sqrt{x^2 + (y+1)^2}$$
$$x^2 + y^2 - 2y + 1 = x^2 + y^2 + 2y + 1$$
$$-4y = 0$$, so $$y = 0$$.
From $$|z + i| = |z - 1|$$:
$$\sqrt{x^2 + (y+1)^2} = \sqrt{(x-1)^2 + y^2}$$
With $$y = 0$$:
$$\sqrt{x^2 + 1} = \sqrt{(x-1)^2}$$
$$x^2 + 1 = x^2 - 2x + 1$$
$$2x = 0$$, so $$x = 0$$.
$$n(S) = 1$$.
Click on the Email ☝️ to Watch the Video Solution
Create a FREE account and get:
Educational materials for JEE preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.
