Write in the form $f(z) = 0$, where $f(z)$ is a polynomial of degree $4$ with real coefficients, the equation having $(3 + i)$ and $(1 + 3i)$ as two of its roots.
Can anyone help me? I'm guessing the two other roots are $(3-i)$ and $(1-3i)$ as they are the complex conjugates of the original roots.
OKAY Thank you for your response, I understand the question and the answer now and I will use that conjugate theorem lots from now on.
Find the real root of the equation $z^3 + z + 10 = 0$ given that one complex root is $1 – 2i$.
I've realised that the roots are $(1-2i), (1+2i)$, and a real number we'll call a
So using the theorem got me $(z-1-2i)(z-1+2i)(z-x)$
No idea on where to go next.