Question

在复数范围内解方程|z^2|+(z+z的共轭复数)i=2-4i/3-i

Answer 1

设z=x+yi(x,y∈R)

|z^2|=x^2+y^2 z+z的共轭复数=2x

2-4i/3-i=(2-4i)(3+i)/10=1-i

x^2+y^2 =1 2x=-1

x=-1/2 y=±√3/2

z=-1/2+√3i/2 z=-1/2-√3i/2