Having trouble with trying to prove this. It looks like it isn't too hard but I can't wrap my head around it.
Let f be a polynomial with real coefficients. Prove: if a complex number z satisfies f(z)=0, then the conjugate of z (call it x) also satisfies f(x)=0
Let the polynomial be of degree n so that...
(1)
If satisfies the condizion that means that is...
(2)
Of course (2) is valid if both the real and imaginary parts of vanish and that's true if we change in (2) with , so that is also a zero of ...
Kind regards