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complex conjugate roots crisis!!:(
Hi,
I'm really stuck on complex conjugate roots!
If z is the root of a polynomial equation then how can you prove that z*(conjugate) is also a root.
e.g Say the polynomial is f(z)=6z^3+11z+6
z=a+bi z*=a−ib If i substitute z into f(z) then i get a real and imaginary part. But when i sub z* the real part the same as in z and the imaginary part is the same except for a change in sign. How can you say that z* is also a root if it has a change of sign when compared to z??? Pls pls help, i really can't make sense of this.
I'm really stuck on complex conjugate roots!
If z is the root of a polynomial equation then how can you prove that z*(conjugate) is also a root.e.g Say the polynomial is f(z)=6z^3+11z+6
z=a+bi z*=a−ib If i substitute z into f(z) then i get a real and imaginary part. But when i sub z* the real part the same as in z and the imaginary part is the same except for a change in sign. How can you say that z* is also a root if it has a change of sign when compared to z??? Pls pls help, i really can't make sense of this.
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