Complex Numbers And Quadratic Equations

...(i)
Squaring (i) both sides, we get


...(ii)
Cubing (ii) both sides, we get



...(iii)
Squaring (iii) both sides we get

We have, and
Let

Now




Equating coefficients of real and imaginary parts, we get
and

We have; ,
and
Now,

Let
or
Let amplitude of be then

or