如何求z的4次方的值

Question

如题所述

Answer 1

z^4=-1,
z^4=[cos(2kπ+π）+isin(2kπ+π)],(k∈Z），
根据棣美弗定理，
z=cos[(2kπ+π）/4]+isin(2kπ+π)/4],(k∈Z），
k=0,
z1=cosπ/4+isinπ/4
=√2/2+√2i/2,
k=1,
z 2=cos3π/4+isin3π/4
=-√2/2+√2i/2,
k=2,
z3=cos5π/4+isin5π/4
=-√2/2-√2i/2,
k=3,
z4=cos7π/4+isin7π/4
=√2/2-√2i/2.