<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def apply_complement(self, a, return_Ya=False):
 """Apply the complementary projection to an array. :param z: array with ``shape==(N,m)``. :return: :math:`P_{\\mathcal{Y}^\\perp,\\mathcal{X}}z = z - P_{\\mathcal{X},\\mathcal{Y}^\\perp} z`. """

        # is projection the zero operator? --> complement is identity
        if self.V.shape[1] == 0:
            if return_Ya:
                return a.copy(), numpy.zeros((0, a.shape[1]))
            return a.copy()
        if return_Ya:
            x, Ya = self._apply(a, return_Ya=True)
        else:
            x = self._apply(a)
        z = a - x
        for i in range(self.iterations-1):
            w = self._apply(z)
            z = z - w
        if return_Ya:
            return z, Ya
        return z