Using r1+r2 will give different answer from r1*r2. Why?
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Daily magic problem July 9th
Daily magic problem July 9th
Re: Daily magic problem July 9th
The sum of the two roots $r_1 + r_2$ must be equal to $-(-5)/1 = 5$, and the product of the roots $r_1r_2$ must be equal to $7 + i$.
Since $(2 + i) + (a + ib) = (2 + a) + (1 + b)i = 5 + 0i$, we must have $2 + a = 5$ and $1 + b = 0$. Similarly, since $(2 + i)(a + ib) = (2a - b)(a + 2b)i = 7 + i$, we must have $2a - b = 7$ and $a + 2b = 1$.
Both systems of equations lead to the same solution $(a,b)$.
Re: Daily magic problem July 9th
Thank you for your explanation! How about using z*(2+i)=7+i Then z=(7+i)/(2+i) This is different. Also, is it ok to use quadratic formula to find solutions? Is it the same?
Re: Daily magic problem July 9th
Note your solution $z = \dfrac{7 + i}{2 + i}$ is the same as $3 - i$: $$\dfrac{7 + i}{2 + i} = \dfrac{7 + i}{2 + i}\dfrac{2-i}{2-i} = \dfrac{15 - 5i}{5} = 3 - i.$$
Using the quadratic formula is always an option, though it can get messy and you wouldn't be taking advantage of the fact that you were given one of the two solutions already.