设w=a+z^6,a∈R,z=[(1-4i)(1+i)+2+4i]/(3+4i),若|w|=10,求a的值_数学解答

设w=a+z^6,a∈R,z=[(1-4i)(1+i)+2+4i]/(3+4i),若|w|=10,求a的值

人气：361 ℃　时间：2020-07-16 21:09:33

解答

z=(1+i-4i+4+2+4i)(3-4i)/(3+4i)(3-4i)
=(7+i)(3-4i)/(9+16)
=(25-25i)/25
=1-i
z^2=(1-i)^2=1-2i-1=-2i
z^6=(-2i)^3=8i
w=a+z^6=a+8i
|w|^2=a^2+64=100
a^2=36
a=(+/-)6