please help with this complex numbers question thank you in advance!?

Z'=a+bi,a,bER,b not =0 is a complex root of the equation Z^2-2Z+25=0.

Without evaulating the roots, answer the following questions:

show that the conjugate of Z' is also a root of Z^2-2Z+25=0

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  • Anonymous
    8 years ago
    Favorite Answer

    Let c + di be the other root of the equation.

    We know the sum of the roots is 2 and the product of the roots is 25

    (a+bi) + (c + di) = 2 + 0i, so b + d = 0. thus d = -b.

    (a+bi)(c+di) = (a + bi)(c - bi) = ac+b^2 +i(bc-ba) = 25 + 0i, so

    bc-ba = 0, or b(c-a) = 0. We are told that b is not 0, so we must have c-a = 0, or c = a

    thus c + di = a - bi, the conjugate of the first root.

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