해법
z5=2−2i
해법
z=421074+10+25−i421074−10+25,z=421074−10−25+i421074+10−25,z=−22107+i22107,z=−421074+10−25−i421074−10−25,z=421074−10+25−i421074+10+25
솔루션 단계
z5=2−2i
위한 zn=a해결책은 zk=n∣a∣(cos(narg(a)+2kπ)+isin(narg(a)+2kπ)),
k=0,1,…,n−1
n=5,a=2−2i 위한∣a∣=2
arg(a)=−4π
z=52(cos(5−4π+2⋅0π)+isin(5−4π+2⋅0π)),z=52(cos(5−4π+2⋅1π)+isin(5−4π+2⋅1π)),z=52(cos(5−4π+2⋅2π)+isin(5−4π+2⋅2π)),z=52(cos(5−4π+2⋅3π)+isin(5−4π+2⋅3π)),z=52(cos(5−4π+2⋅4π)+isin(5−4π+2⋅4π))
52(cos(5−4π+2⋅0π)+isin(5−4π+2⋅0π))단순화하세요:421074+10+25−i421074−10+25
52(cos(5−4π+2⋅1π)+isin(5−4π+2⋅1π))단순화하세요:421074−10−25+i421074+10−25
52(cos(5−4π+2⋅2π)+isin(5−4π+2⋅2π))단순화하세요:−22107+i22107
52(cos(5−4π+2⋅3π)+isin(5−4π+2⋅3π))단순화하세요:−421074+10−25−i421074−10−25
52(cos(5−4π+2⋅4π)+isin(5−4π+2⋅4π))단순화하세요:421074−10+25−i421074+10+25
z=421074+10+25−i421074−10+25,z=421074−10−25+i421074+10−25,z=−22107+i22107,z=−421074+10−25−i421074−10−25,z=421074−10+25−i421074+10+25