Basis (Y)

Test for Linearly Independent

$\frac{1}{\sqrt{2}}x+\frac{1}{\sqrt{2}}iy=0$
$\frac{1}{\sqrt{2}}x-\frac{1}{\sqrt{2}}iy=0$

II + I: $2\cdot \frac{1}{\sqrt{2}}x=0$ => x = 0
Einsetzten: $\frac{1}{\sqrt{2}}iy=0$ => iy = 0