Question

Expresse z na forma algébrica x= 1+i/1+2i + 1+i/i

Answer 1

Explicação passo-a-passo:

$\sf z=\dfrac{1+i}{1+2i}+\dfrac{1+i}{i}$

$\sf z=\dfrac{(1+i)\cdot i+(1+2i)\cdot(1+i)}{(1+2i)\cdot i}$

$\sf z=\dfrac{i+i^2+1+i+2i+2i^2}{i+2i^2}$

$\sf z=\dfrac{i-1+1+3i-2}{i-2}$

$\sf z=\dfrac{-2+4i}{-2+i}$

$\sf z=\dfrac{-2+4i}{-2+i}\cdot\dfrac{-2-i}{-2-i}$

$\sf z=\dfrac{4+2i-8i-4i^2}{(-2)^2-i^2}$

$\sf z=\dfrac{4-6i+4}{4+1}$

$\sf z=\dfrac{8-6i}{5}$

$\sf z=\dfrac{8}{5}-\dfrac{6i}{5}$