6 Find the complex numbers \(w\) which satisfy the equation \(w ^ { 2 } + 2 \mathrm { i } w ^ { * } = 1\) and are such that \(\operatorname { Re } w \leqslant 0\). Give your answers in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.