设f(z)=(1/5)z^5-(1+i)z,求方程f'(z)=0的所有根

Question

设f(z)=(1/5)z^5-(1+i)z,求方程f'(z)=0的所有根

Answer 1

f'(z)=z^4-(1+i)=0
z^4=1+i
z^2=±(1+i)^1/2
即z^2=(1+i)^1/2 或z^2=-(1+i)^1/2=i^2 * (1+i)^1/2
z=±(1+i)^1/4 或z=±i(1+i)^1/4