Question

设i为虚数单位，则1-i+i²-i³+i⁴-…+i²⁰=______．

Answer 1

1-i+i²-i³+i⁴-…+i²⁰=

1-(-i)21

1+i

=

1+i21

1+i

=

1+i

1+i

=1．
故答案为：1．