For the cubic equation z^3+az^2+3z+9 where one zero is purely imaginary.
I factorized into (z-a)(z-bi)(z+bi)
And on to expand and equate coefficients to get a=3, and b = +/-sqrt(3)
Now to write back the cubic equation as a product of linear factors, how do I write b?
The answer is
(z-a)(z+sqrt(3)i)(z-sqrt(3)i)
But why?
Isn't it
(z-a)(z+sqrt(3))(z-sqrt(3)i) since one of the roots is a positive sqrt(3)?
Thank you so much!