Resposta:

C) z=-1+i

Explicação passo-a-passo:

[tex]z = \sqrt{2} (cos135 + i.sen135) = \\ z = \sqrt{2} (cos135)+ i \times sen(135) \\ z = \sqrt{2}( \frac{2}{2} + isin(135) \\ z \sqrt{2} (cos(135) + 1 \times sin(135) \\ z = \sqrt{2} ( \frac{ \sqrt{2} }{2} + i \times \frac{ \sqrt{2} }{2} \\ z = \sqrt{2} ( \frac{ - \sqrt{2} }{2} + \frac{ \sqrt{2} }{2}i \\ - \sqrt{2} \times \frac{ \sqrt{2} }{2} + \sqrt{2} \times \frac{ \sqrt{2} }{2}i \\ - \frac{2}{2} + \sqrt{2} \times \frac{ \sqrt{2} }{2}i \\ - \sqrt{2} \times \frac{ \sqrt{2} }{2} \times \sqrt{2} \times \frac{ \sqrt{2} }{2}i \\ - \frac{2}{2} + \frac{2}{2} \\ - \frac{2}{2} + \frac{2}{2}aqui \\ risque \: os \: dois \: primeiros \: numeros \: 2 \: e \: 2 \\ - 1 + \frac{2}{2}i \\ z = \sqrt{2}( \frac{ \sqrt{2} }{ - 2} + \frac{ \sqrt{2} }{2}i) \\ z = - 1+i\\ resposta \\ z = - 1 + i[/tex]