Conjugating complex root

Algebra Level 4

If x+ιy=±(a+ιb \large \displaystyle \sqrt{x + \iota y} = \pm (a + \iota b), then xιy = ?\large \displaystyle \sqrt{ x - \iota y}\ = \ ?

Clarification : ι=1\iota = \sqrt{-1}

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