Question

当z=(1-i)/(√2)时,z的一百次方+z的50次方+1的值是多少? 为什么?

Answer 1

z=1/√2-i/√2＝cos(-π/4)+isin(-π/4)
因此
z^100=[cos(-π/4)+isin(-π/4)]^100
=cos(-π/4*100)+isin(-π/4*100)
=cos(-25π)+isin(-25π)
=-1-i
所以z^100+1=-i.