z=√2/(1-i)=(√2/2)(1+i)
z²=(√2/2)²(1+i)²=(1/2)(1+2i-1)=i
z⁴=(z²)²=i²=-1
z^100+z^50+1
=(z⁴)^25 +[(z⁴)^12]×z²+1
=(-1)^25+[(-1)^12]i +1
=-1+i+1
=i
选D.