conjugated roots of equation
concerning the complex conjugates of the sum and product of two complex numbers, may be by induction generalised for arbitrary number of complex numbers . Since the complex conjugate of a real number is the same real number, we may write
for real numbers . Thus, for a polynomial we obtain
I.e., the values of a polynomial with real coefficients computed at a complex number and its complex conjugate are complex conjugates of each other.
If especially the value of a polynomial with real coefficients vanishes at some complex number , it vanishes also at . So the roots of an algebraic equation
with real coefficients are pairwise complex conjugate numbers.
Example. The roots of the binomial equation
are , , the third roots of unity.
|Title||conjugated roots of equation|
|Date of creation||2013-03-22 17:36:51|
|Last modified on||2013-03-22 17:36:51|
|Last modified by||pahio (2872)|
|Synonym||roots of algebraic equation with real coefficients|