解答
z5=−1−i
解答
z=42534+10−25−i42534−10−25,z=2253+i2253,z=−42534−10−25+i42534+10−25,z=−42534+10+25−i42534−10+25,z=−42534−10+25−i42534+10+25
求解步骤
z5=−1−i
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=−1−i∣a∣=2
arg(a)=4π−π
z=52(cos(54π−π+2⋅0π)+isin(54π−π+2⋅0π)),z=52(cos(54π−π+2⋅1π)+isin(54π−π+2⋅1π)),z=52(cos(54π−π+2⋅2π)+isin(54π−π+2⋅2π)),z=52(cos(54π−π+2⋅3π)+isin(54π−π+2⋅3π)),z=52(cos(54π−π+2⋅4π)+isin(54π−π+2⋅4π))
化简 52(cos(54π−π+2⋅0π)+isin(54π−π+2⋅0π)):42534+10−25−i42534−10−25
化简 52(cos(54π−π+2⋅1π)+isin(54π−π+2⋅1π)):2253+i2253
化简 52(cos(54π−π+2⋅2π)+isin(54π−π+2⋅2π)):−42534−10−25+i42534+10−25
化简 52(cos(54π−π+2⋅3π)+isin(54π−π+2⋅3π)):−42534+10+25−i42534−10+25
化简 52(cos(54π−π+2⋅4π)+isin(54π−π+2⋅4π)):−42534−10+25−i42534+10+25
z=42534+10−25−i42534−10−25,z=2253+i2253,z=−42534−10−25+i42534+10−25,z=−42534+10+25−i42534−10+25,z=−42534−10+25−i42534+10+25