Question

determine os complexos u e v tais que u+v=2-5i e u-2v= -4+13i.

Answer 1

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$\left \{ {{v+u=2-5i} \atop {u-2v=-4+13i}} \right.$

isola

u=2-5i-v

subst/ em

$u-2v=-4+13i \\ 2-5i-v-2v=-4+13i \\ -3v=-4+13i-2+5i \\- 3v=-6+18i \\ 3v=6-18i$

$v= \frac{6-18i}{3} = \frac{3(2-6i)}{3} =2-6i$

como
$u=2-5i-v \\ u=2-5i-(2-6i) \\ u=2-5i-2+6i \\ u=i$

Logo
$v=2-6i \\ u=i$