If $z=x+iy$ is a complex number satisfying $\left|z+\frac{i}{2}\right|^2=\left|z-\frac{i}{2}\right|^2$,then the locus of $z$ is

  • A
    $x$-axis
  • B
    $y$-axis
  • C
    $y=x$
  • D
    $2y=x$

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