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 z3 + 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.