若z=根号2/1-i,则z^100+z^50+1的值是A.1 B.-1C.-iD.i
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若z=根号2/1-i,则z^100+z^50+1的值是A.1B.-1C.-iD.i若z=根号2/1-i,则z^100+z^50+1的值是A.1B.-1C.-iD.i若z=根号2/1-i,则z^100+
若z=根号2/1-i,则z^100+z^50+1的值是A.1 B.-1C.-iD.i
若z=根号2/1-i
A.1
B.-1
C.-i
D.i
若z=根号2/1-i,则z^100+z^50+1的值是A.1 B.-1C.-iD.i
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.
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