$Im(z_1)>0$ applies to all but the point on the x axis
$z_2 = 10z_1$ means that $|z_2| = 10|z_1|$
$Re(z_3) = 0$ means $z_3$ lies on the imaginary axis. This is the point you've labeled $z_4$
$Im(z_4) = 0$ means $z_4$ lies on the real axis. This is the point you've labeled $z_3$
So we've got $z_3,~z_4$ figured out.
$z_1,~z_2$ must be as you've labeled them.
So swap, $z_3, ~z_4$ and you're good.