Question

Determine a e b, respectivamente, de modo que ( 1 – 2i)/ 3 + i3 = a + bi
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Answer 1

Explicação passo-a-passo:

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

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

$\sf =\dfrac{3+i-6i-2i^2}{3^2-i^2}$

$\sf =\dfrac{3-5i-2\cdot(-1)}{9-(-1)}$

$\sf =\dfrac{3-5i+2}{9+1}$

$\sf =\dfrac{5-5i}{10}$

$\sf =\dfrac{5}{10}-\dfrac{5i}{10}$

$\sf =\dfrac{1}{2}-\dfrac{i}{2}$

$\sf =a+bi$

Assim:

$\sf a=\dfrac{1}{2}~e~b=\dfrac{-1}{2}$