解答
z5=4−4i
解答
z=24+10+25−i24−10+25,z=24−10−25+i24+10−25,z=−1+i,z=−24+10−25−i24−10−25,z=24−10+25−i24+10+25
求解步骤
z5=4−4i
For zn=athe solutions are zk=n∣a∣(cos(narg(a)+2kπ)+isin(narg(a)+2kπ)),
k=0,1,…,n−1
对于 n=5,a=4−4i∣a∣=42
arg(a)=−4π
z=542(cos(5−4π+2⋅0π)+isin(5−4π+2⋅0π)),z=542(cos(5−4π+2⋅1π)+isin(5−4π+2⋅1π)),z=542(cos(5−4π+2⋅2π)+isin(5−4π+2⋅2π)),z=542(cos(5−4π+2⋅3π)+isin(5−4π+2⋅3π)),z=542(cos(5−4π+2⋅4π)+isin(5−4π+2⋅4π))
化简 542(cos(5−4π+2⋅0π)+isin(5−4π+2⋅0π)):24+10+25−i24−10+25
化简 542(cos(5−4π+2⋅1π)+isin(5−4π+2⋅1π)):24−10−25+i24+10−25
化简 542(cos(5−4π+2⋅2π)+isin(5−4π+2⋅2π)):−1+i
化简 542(cos(5−4π+2⋅3π)+isin(5−4π+2⋅3π)):−24+10−25−i24−10−25
化简 542(cos(5−4π+2⋅4π)+isin(5−4π+2⋅4π)):24−10+25−i24+10+25
z=24+10+25−i24−10+25,z=24−10−25+i24+10−25,z=−1+i,z=−24+10−25−i24−10−25,z=24−10+25−i24+10+25