Conjugate Complex Numbers

Conjugate Complex Numbers

 

two complex numbers of the form z = a + bi and z̄ = a- bi, where Conjugate Complex Numbers. Conjugate complex numbers are the roots of the quadratic equation

z2 – 2 az + a2 + b 2 = 0

with real coefficients. The sum and the product of two conjugate complex numbers are real. The conjugate of a sum is equal to the sum of the conjugates of the summands, and the conjugate of a product is equal to the product of the conjugates of the factors: Conjugate Complex Numbers. If z is a root of a polynomial with real coefficients, then z is also a root of the polynomial and is of the same multiplicity as z.

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If the characteristic polynomial has a pair of conjugate complex numbers, the moduli of conjugate complex numbers are less than one.
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The sum of two conjugate complex numbers is always ...?