Question

Solve the equation : 2│z│ 2 + z 2 – 5 + i√3 = 0.

Answer 1

we know
|z|=root (x^2+y^2)
where x is real number and y is imaginary number
now
|z|^2+z^2-5+iroot3=0

=> x^2+y^2+(x+iy)(x+iy)-5+iroot3=0

=> x^2+y^2+x^2-y^2+2ixy-5+iroot3=0

=>(2x^2-5)+i(2xy+root3)=0
now
2x^2-5=0
x=+_root (5/2)
and also 2xy+root3=0 put x value and find y
y=_+root (3/10)