If $|z+i|-|z-1|=|z|-2=0$ for a complex number $z$, then $z=$

• A

  $\sqrt{2}(1+i)$
• Correct answer
  B

  $\sqrt{2}(1-i)$
• Correct answer
  C

  $\sqrt{2}(-1+i)$
• D

  $\sqrt{2}(-1-\mathrm{i})$

Solution

$|z| =2$ represents circle
$|z+i|=|z-1|$ represents
Solving $x^{2}+y^{2}=4$ and $y=-x$
$z=\sqrt{2}(1-i), \quad \sqrt{2}(-1+i)$

Hence, the correct answer is options: 'B', 'C'.