If a complex number z statisfies the equation x+√2|z+1|+i=0, then |z| is equal to :
JEE Main 2013 — Mathematics Algebra
2013mcqhard
If a complex number z statisfies the equation x+2∣z+1∣+i=0, then ∣z∣ is equal to :
Official previous-year question
Held on 22 Apr 2013 · Verified 6 Jul 2026.
Options
A
2
B
3
C
5
D
1
Did you get this right?
Sign in to track your attempts and accuracy.
Solution
Given equation is z+2∣z+1∣+i=0 put z=x+iy in the given equation. (x+iy)+2∣x+iy+1∣+i=0⇒x+iy+2[(x+1)2+y2]+i=0 Now, equating real and imaginary part, we get x+2(x+1)2+y2=0 and y+1=0⇒y=−1⇒x+2(x+1)2+(−1)2=0⇒2(x+1)2+1=−x⇒2[(x+1)2+1]=x2⇒x2+4x+4=0⇒x=−2 Thus, z=−2+i(−1)⇒∣z∣=5
Your note
Sign in to keep a private note on this question. Nothing you write is ever public.