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
- Anonymous8 years agoFavorite 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.