Q: If |z| = min {|z – 1|, |z + 1|}, then
(A) |z + z–| = 1/2
(B) z + z– = 1
(C) |z + z–| = 1
(D) none of these
Click to See Answer :
Ans: (C)
Sol: Sol. |z| = min {|z – 1|, |z + 1|} = |z – 1| for Re (z) > 0
But |z| = |z – 1| ⇒ Re (z) = 1/2 ,
Similarly, |z| = min {|z – 1|, |z + 1|} = |z + 1|, for Re (z) < 0
⇒ |z| = |z + 1| ⇒ Re (z) = -1/2
where Re(z) =1/2 , z + z– = 1 , |z + z–| = 1
when Re (z) = 0 ⇒ z + z– = 0 and z + z– = 0
Hence the argument is |z + z– | = 1
Hence (C) is the correct answer.